diff --git a/test-crates/pyo3-no-extension-module/Cargo.lock b/test-crates/pyo3-no-extension-module/Cargo.lock
index 769600ce4..abb6f46bc 100644
--- a/test-crates/pyo3-no-extension-module/Cargo.lock
+++ b/test-crates/pyo3-no-extension-module/Cargo.lock
@@ -38,9 +38,9 @@ dependencies = [
 
 [[package]]
 name = "memoffset"
-version = "0.8.0"
+version = "0.9.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d61c719bcfbcf5d62b3a09efa6088de8c54bc0bfcd3ea7ae39fcc186108b8de1"
+checksum = "5a634b1c61a95585bd15607c6ab0c4e5b226e695ff2800ba0cdccddf208c406c"
 dependencies = [
  "autocfg",
 ]
@@ -76,9 +76,9 @@ dependencies = [
 
 [[package]]
 name = "pyo3"
-version = "0.18.1"
+version = "0.19.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "06a3d8e8a46ab2738109347433cb7b96dffda2e4a218b03ef27090238886b147"
+checksum = "cffef52f74ec3b1a1baf295d9b8fcc3070327aefc39a6d00656b13c1d0b8885c"
 dependencies = [
  "cfg-if",
  "libc",
@@ -90,9 +90,9 @@ dependencies = [
 
 [[package]]
 name = "pyo3-build-config"
-version = "0.18.1"
+version = "0.19.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "75439f995d07ddfad42b192dfcf3bc66a7ecfd8b4a1f5f6f046aa5c2c5d7677d"
+checksum = "713eccf888fb05f1a96eb78c0dbc51907fee42b3377272dc902eb38985f418d5"
 dependencies = [
  "once_cell",
  "target-lexicon",
@@ -100,9 +100,9 @@ dependencies = [
 
 [[package]]
 name = "pyo3-ffi"
-version = "0.18.1"
+version = "0.19.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "839526a5c07a17ff44823679b68add4a58004de00512a95b6c1c98a6dcac0ee5"
+checksum = "5b2ecbdcfb01cbbf56e179ce969a048fd7305a66d4cdf3303e0da09d69afe4c3"
 dependencies = [
  "libc",
  "pyo3-build-config",
diff --git a/tests/common/integration.rs b/tests/common/integration.rs
index 17493d64b..e3bc2d566 100644
--- a/tests/common/integration.rs
+++ b/tests/common/integration.rs
@@ -3,7 +3,7 @@ use anyhow::{bail, Context, Result};
 #[cfg(feature = "zig")]
 use cargo_zigbuild::Zig;
 use clap::Parser;
-use maturin::{BuildOptions, PythonInterpreter};
+use maturin::{BuildOptions, PlatformTag, PythonInterpreter};
 use std::env;
 use std::path::Path;
 use std::process::Command;
@@ -93,14 +93,19 @@ pub fn test_integration(
     // We can do this since we know that wheels are built and returned in the
     // order they are in the build context
     for ((filename, supported_version), python_interpreter) in wheels.iter().zip(interpreter) {
-        if test_zig && build_context.target.is_linux() && !build_context.target.is_musl_target() {
+        if test_zig
+            && build_context.target.is_linux()
+            && !build_context.target.is_musl_target()
+            && build_context.target.get_minimum_manylinux_tag() != PlatformTag::Linux
+        {
             let rustc_ver = rustc_version::version()?;
+            let python_arch = build_context.target.get_python_arch();
             let file_suffix = if rustc_ver >= semver::Version::new(1, 64, 0) {
-                "manylinux_2_17_x86_64.manylinux2014_x86_64.whl"
+                format!("manylinux_2_17_{python_arch}.manylinux2014_{python_arch}.whl")
             } else {
-                "manylinux_2_12_x86_64.manylinux2010_x86_64.whl"
+                format!("manylinux_2_12_{python_arch}.manylinux2010_{python_arch}.whl")
             };
-            assert!(filename.to_string_lossy().ends_with(file_suffix))
+            assert!(filename.to_string_lossy().ends_with(&file_suffix))
         }
         let mut venv_name = if supported_version == "py3" {
             format!("{unique_name}-py3")