diff --git a/packages/core/__tests__/cli/custom-extensions.test.ts b/packages/core/__tests__/cli/custom-extensions.test.ts
index 56a74db52..ec01eabd1 100644
--- a/packages/core/__tests__/cli/custom-extensions.test.ts
+++ b/packages/core/__tests__/cli/custom-extensions.test.ts
@@ -3,6 +3,8 @@ import { stripIndent } from 'common-tags';
 import stripAnsi = require('strip-ansi');
 import { describe, beforeEach, afterEach, test, expect } from 'vitest';
 import { Project } from 'glint-monorepo-test-utils';
+import typescript from 'typescript';
+import semver from 'semver';
 
 describe('CLI: custom extensions', () => {
   let project!: Project;
@@ -121,4 +123,47 @@ describe('CLI: custom extensions', () => {
       await watch.terminate();
     });
   });
+
+  describe('module resolution with explicit extensions', () => {
+    beforeEach(() => {
+      project.setGlintConfig({ environment: 'ember-template-imports' });
+      project.write({
+        'index.gts': stripIndent`
+          import Greeting from './Greeting.gts';
+          <template><Greeting /></template>
+        `,
+        'Greeting.gts': stripIndent`
+          <template>Hello!</template>
+        `,
+      });
+    });
+
+    test('is illegal by default', async () => {
+      let result = await project.check({ reject: false });
+
+      expect(result.exitCode).toBe(1);
+      expect(stripAnsi(result.stderr)).toMatchInlineSnapshot(`
+        "index.gts:1:22 - error TS2307: Cannot find module './Greeting.gts' or its corresponding type declarations.
+
+        1 import Greeting from './Greeting.gts';
+                               ~~~~~~~~~~~~~~~~
+        "
+      `);
+    });
+
+    test.runIf(semver.gte(typescript.version, '5.0.0'))(
+      'works with `allowImportingTsExtensions: true`',
+      async () => {
+        project.updateTsconfig((config) => {
+          config.compilerOptions ??= {};
+          config.compilerOptions['allowImportingTsExtensions'] = true;
+        });
+
+        let result = await project.check();
+
+        expect(result.exitCode).toBe(0);
+        expect(result.stderr).toBe('');
+      }
+    );
+  });
 });
diff --git a/packages/core/__tests__/language-server/custom-extensions.test.ts b/packages/core/__tests__/language-server/custom-extensions.test.ts
index 50c3285b1..30b5b1aac 100644
--- a/packages/core/__tests__/language-server/custom-extensions.test.ts
+++ b/packages/core/__tests__/language-server/custom-extensions.test.ts
@@ -1,6 +1,8 @@
 import { Project } from 'glint-monorepo-test-utils';
 import { describe, beforeEach, afterEach, test, expect } from 'vitest';
 import { stripIndent } from 'common-tags';
+import typescript from 'typescript';
+import semver from 'semver';
 
 describe('Language Server: custom file extensions', () => {
   let project!: Project;
@@ -254,4 +256,59 @@ describe('Language Server: custom file extensions', () => {
       ]);
     });
   });
+
+  describe('module resolution with explicit extensions', () => {
+    beforeEach(() => {
+      project.setGlintConfig({ environment: 'ember-template-imports' });
+      project.write({
+        'index.gts': stripIndent`
+          import Greeting from './Greeting.gts';
+          <template><Greeting /></template>
+        `,
+        'Greeting.gts': stripIndent`
+          <template>Hello!</template>
+        `,
+      });
+    });
+
+    test('is illegal by default', async () => {
+      let server = project.startLanguageServer();
+
+      expect(server.getDiagnostics(project.fileURI('index.gts'))).toMatchInlineSnapshot(`
+        [
+          {
+            "code": 2307,
+            "message": "Cannot find module './Greeting.gts' or its corresponding type declarations.",
+            "range": {
+              "end": {
+                "character": 37,
+                "line": 0,
+              },
+              "start": {
+                "character": 21,
+                "line": 0,
+              },
+            },
+            "severity": 1,
+            "source": "glint",
+            "tags": [],
+          },
+        ]
+      `);
+    });
+
+    test.runIf(semver.gte(typescript.version, '5.0.0'))(
+      'works with `allowImportingTsExtensions: true`',
+      async () => {
+        project.updateTsconfig((config) => {
+          config.compilerOptions ??= {};
+          config.compilerOptions['allowImportingTsExtensions'] = true;
+        });
+
+        let server = project.startLanguageServer();
+
+        expect(server.getDiagnostics(project.fileURI('index.gts'))).toEqual([]);
+      }
+    );
+  });
 });
diff --git a/packages/core/src/cli/perform-build-watch.ts b/packages/core/src/cli/perform-build-watch.ts
index 7c6f5b92d..8444ecc7a 100644
--- a/packages/core/src/cli/perform-build-watch.ts
+++ b/packages/core/src/cli/perform-build-watch.ts
@@ -10,7 +10,7 @@ export function performBuildWatch(
   projects: string[],
   buildOptions: TS.BuildOptions
 ): void {
-  let transformManagerPool = new TransformManagerPool(ts.sys);
+  let transformManagerPool = new TransformManagerPool(ts);
   let formatDiagnostic = buildDiagnosticFormatter(ts);
   let buildProgram = ts.createEmitAndSemanticDiagnosticsBuilderProgram;
 
@@ -20,6 +20,9 @@ export function performBuildWatch(
     (diagnostic) => console.error(formatDiagnostic(diagnostic))
   );
 
+  // @ts-ignore: This hook was added in TS5, and is safely irrelevant in earlier versions. Once we drop support for 4.x, we can also remove this @ts-ignore comment.
+  host.resolveModuleNameLiterals = transformManagerPool.resolveModuleNameLiterals;
+
   let builder = ts.createSolutionBuilderWithWatch(host, projects, buildOptions);
   builder.build();
 }
diff --git a/packages/core/src/cli/perform-build.ts b/packages/core/src/cli/perform-build.ts
index 52b91bd36..9b5ac3379 100644
--- a/packages/core/src/cli/perform-build.ts
+++ b/packages/core/src/cli/perform-build.ts
@@ -13,7 +13,7 @@ interface BuildOptions extends TS.BuildOptions {
 }
 
 export function performBuild(ts: TypeScript, projects: string[], buildOptions: BuildOptions): void {
-  let transformManagerPool = new TransformManagerPool(ts.sys);
+  let transformManagerPool = new TransformManagerPool(ts);
   let formatDiagnostic = buildDiagnosticFormatter(ts);
   let buildProgram = ts.createEmitAndSemanticDiagnosticsBuilderProgram;
 
@@ -23,6 +23,9 @@ export function performBuild(ts: TypeScript, projects: string[], buildOptions: B
     (diagnostic) => console.error(formatDiagnostic(diagnostic))
   );
 
+  // @ts-ignore: This hook was added in TS5, and is safely irrelevant in earlier versions. Once we drop support for 4.x, we can also remove this @ts-ignore comment.
+  host.resolveModuleNameLiterals = transformManagerPool.resolveModuleNameLiterals;
+
   let builder = ts.createSolutionBuilder(host, projects, buildOptions);
   let exitStatus = buildOptions.clean ? builder.clean() : builder.build();
   process.exit(exitStatus);
diff --git a/packages/core/src/cli/perform-check.ts b/packages/core/src/cli/perform-check.ts
index 58c026053..3de364b76 100644
--- a/packages/core/src/cli/perform-check.ts
+++ b/packages/core/src/cli/perform-check.ts
@@ -63,6 +63,8 @@ function createCompilerHost(
     ? ts.createIncrementalCompilerHost(options, sysForCompilerHost(ts, transformManager))
     : ts.createCompilerHost(options);
 
+  // @ts-ignore: This hook was added in TS5, and is safely irrelevant in earlier versions. Once we drop support for 4.x, we can also remove this @ts-ignore comment.
+  host.resolveModuleNameLiterals = transformManager.resolveModuleNameLiterals;
   host.fileExists = transformManager.fileExists;
   host.readFile = transformManager.readTransformedFile;
   host.readDirectory = transformManager.readDirectory;
diff --git a/packages/core/src/cli/perform-watch.ts b/packages/core/src/cli/perform-watch.ts
index 3a2b5dd0e..36608f5d1 100644
--- a/packages/core/src/cli/perform-watch.ts
+++ b/packages/core/src/cli/perform-watch.ts
@@ -19,5 +19,8 @@ export function performWatch(glintConfig: GlintConfig, optionsToExtend: ts.Compi
     (diagnostic) => console.error(formatDiagnostic(diagnostic))
   );
 
+  // @ts-ignore: This hook was added in TS5, and is safely irrelevant in earlier versions. Once we drop support for 4.x, we can also remove this @ts-ignore comment.
+  host.resolveModuleNameLiterals = transformManager.resolveModuleNameLiterals;
+
   ts.createWatchProgram(host);
 }
diff --git a/packages/core/src/cli/utils/transform-manager-pool.ts b/packages/core/src/cli/utils/transform-manager-pool.ts
index 035f0652e..5aa6f769e 100644
--- a/packages/core/src/cli/utils/transform-manager-pool.ts
+++ b/packages/core/src/cli/utils/transform-manager-pool.ts
@@ -17,6 +17,7 @@ import { assert } from './assert.js';
  *   config.
  */
 export default class TransformManagerPool {
+  #rootTS: typeof TS;
   #rootSys: TS.System;
   #managers = new Map<GlintConfig, TransformManager>();
   #loader = new ConfigLoader();
@@ -25,8 +26,9 @@ export default class TransformManagerPool {
     return true;
   }
 
-  constructor(sys: TS.System) {
-    this.#rootSys = sys;
+  constructor(ts: typeof TS) {
+    this.#rootTS = ts;
+    this.#rootSys = ts.sys;
   }
 
   public managerForFile(path: string): TransformManager | null {
@@ -45,6 +47,34 @@ export default class TransformManagerPool {
     return manager;
   }
 
+  public resolveModuleNameLiterals = (
+    moduleLiterals: readonly TS.StringLiteralLike[],
+    containingFile: string,
+    redirectedReference: TS.ResolvedProjectReference | undefined,
+    options: TS.CompilerOptions
+  ): readonly TS.ResolvedModuleWithFailedLookupLocations[] => {
+    let resolveModuleNameLiterals = this.managerForFile(containingFile)?.resolveModuleNameLiterals;
+    if (resolveModuleNameLiterals) {
+      return resolveModuleNameLiterals(
+        moduleLiterals,
+        containingFile,
+        redirectedReference,
+        options
+      );
+    } else {
+      return moduleLiterals.map((literal) =>
+        this.#rootTS.resolveModuleName(
+          literal.text,
+          containingFile,
+          options,
+          this.#rootSys,
+          undefined,
+          redirectedReference
+        )
+      );
+    }
+  };
+
   public readDirectory = (
     rootDir: string,
     extensions: ReadonlyArray<string>,
diff --git a/packages/core/src/common/transform-manager.ts b/packages/core/src/common/transform-manager.ts
index 9530aec46..fd849f0e3 100644
--- a/packages/core/src/common/transform-manager.ts
+++ b/packages/core/src/common/transform-manager.ts
@@ -21,13 +21,25 @@ type TransformInfo = {
 
 export default class TransformManager {
   private transformCache = new Map<string, TransformInfo>();
+  private moduleResolutionHost: ts.ModuleResolutionHost;
   private readonly ts: typeof import('typescript');
 
+  public readonly moduleResolutionCache: ts.ModuleResolutionCache;
+
   constructor(
     private glintConfig: GlintConfig,
     private documents: DocumentCache = new DocumentCache(glintConfig)
   ) {
     this.ts = glintConfig.ts;
+    this.moduleResolutionCache = this.ts.createModuleResolutionCache(
+      this.ts.sys.getCurrentDirectory(),
+      (name) => name
+    );
+    this.moduleResolutionHost = {
+      ...this.ts.sys,
+      readFile: this.readTransformedFile,
+      fileExists: this.fileExists,
+    };
   }
 
   public getTransformDiagnostics(fileName?: string): Array<Diagnostic> {
@@ -161,6 +173,32 @@ export default class TransformManager {
     return { transformedFileName, transformedOffset };
   }
 
+  public resolveModuleNameLiterals = (
+    moduleLiterals: readonly ts.StringLiteralLike[],
+    containingFile: string,
+    redirectedReference: ts.ResolvedProjectReference | undefined,
+    options: ts.CompilerOptions
+  ): readonly ts.ResolvedModuleWithFailedLookupLocations[] => {
+    return moduleLiterals.map((literal) => {
+      // If import paths are allowed to include TS extensions (`.ts`, `.tsx`, etc), then we want to
+      // ensure we normalize things like `.gts` to the standard script path we present elsewhere so
+      // that TS understands the intent.
+      // @ts-ignore: this flag isn't available in the oldest versions of TS we support
+      let scriptPath = options.allowImportingTsExtensions
+        ? this.getScriptPathForTS(literal.text)
+        : literal.text;
+
+      return this.ts.resolveModuleName(
+        scriptPath,
+        containingFile,
+        options,
+        this.moduleResolutionHost,
+        this.moduleResolutionCache,
+        redirectedReference
+      );
+    });
+  };
+
   public watchTransformedFile = (
     path: string,
     originalCallback: ts.FileWatcherCallback,
@@ -175,6 +213,8 @@ export default class TransformManager {
     let { glintConfig, documents } = this;
     let callback: ts.FileWatcherCallback = (watchedPath, eventKind) => {
       if (eventKind === this.ts.FileWatcherEventKind.Deleted) {
+        // Adding or removing a file invalidates most of what we think we know about module resolution
+        this.moduleResolutionCache.clear();
         this.documents.removeDocument(watchedPath);
       } else {
         this.documents.markDocumentStale(watchedPath);
@@ -213,8 +253,11 @@ export default class TransformManager {
       throw new Error('Internal error: TS `watchDirectory` unavailable');
     }
 
-    let callback: ts.DirectoryWatcherCallback = (filename) =>
+    let callback: ts.DirectoryWatcherCallback = (filename) => {
+      // Adding or removing a file invalidates most of what we think we know about module resolution
+      this.moduleResolutionCache.clear();
       originalCallback(this.getScriptPathForTS(filename));
+    };
 
     return this.ts.sys.watchDirectory(path, callback, recursive, options);
   };
diff --git a/packages/core/src/language-server/glint-language-server.ts b/packages/core/src/language-server/glint-language-server.ts
index a1b37d945..038662e3d 100644
--- a/packages/core/src/language-server/glint-language-server.ts
+++ b/packages/core/src/language-server/glint-language-server.ts
@@ -77,6 +77,8 @@ export default class GlintLanguageServer {
       fileExists: this.transformManager.fileExists,
       readFile: this.transformManager.readTransformedFile,
       readDirectory: this.transformManager.readDirectory,
+      // @ts-ignore: This hook was added in TS5, and is safely irrelevant in earlier versions. Once we drop support for 4.x, we can also remove this @ts-ignore comment.
+      resolveModuleNameLiterals: this.transformManager.resolveModuleNameLiterals,
       getCompilationSettings: () => parsedConfig.options,
       // Yes, this looks like a mismatch, but built-in lib declarations don't resolve
       // correctly otherwise, and this is what the TS wiki uses in their code snippet.
@@ -119,6 +121,9 @@ export default class GlintLanguageServer {
     if (filePath.startsWith(this.glintConfig.rootDir)) {
       this.rootFileNames.add(this.transformManager.getScriptPathForTS(filePath));
     }
+
+    // Adding or removing a file invalidates most of what we think we know about module resolution.
+    this.transformManager.moduleResolutionCache.clear();
   }
 
   public watchedFileDidChange(uri: string): void {
@@ -136,6 +141,9 @@ export default class GlintLanguageServer {
     if (!companionPath || this.glintConfig.getSynthesizedScriptPathForTS(companionPath) !== path) {
       this.rootFileNames.delete(this.glintConfig.getSynthesizedScriptPathForTS(path));
     }
+
+    // Adding or removing a file invalidates most of what we think we know about module resolution.
+    this.transformManager.moduleResolutionCache.clear();
   }
 
   public getDiagnostics(uri: string): Array<Diagnostic> {
diff --git a/test-packages/ts-ember-app/types/global.d.ts b/test-packages/ts-ember-app/types/global.d.ts
deleted file mode 100644
index e9a022fef..000000000
--- a/test-packages/ts-ember-app/types/global.d.ts
+++ /dev/null
@@ -1,6 +0,0 @@
-// Types for compiled templates
-declare module 'ts-ember-app/templates/*' {
-  import { TemplateFactory } from 'htmlbars-inline-precompile';
-  const tmpl: TemplateFactory;
-  export default tmpl;
-}
diff --git a/test-packages/ts-ember-preview-types/types/global.d.ts b/test-packages/ts-ember-preview-types/types/global.d.ts
deleted file mode 100644
index e9a022fef..000000000
--- a/test-packages/ts-ember-preview-types/types/global.d.ts
+++ /dev/null
@@ -1,6 +0,0 @@
-// Types for compiled templates
-declare module 'ts-ember-app/templates/*' {
-  import { TemplateFactory } from 'htmlbars-inline-precompile';
-  const tmpl: TemplateFactory;
-  export default tmpl;
-}