diff --git a/lib/internal/streams/pipeline.js b/lib/internal/streams/pipeline.js
index bb34759b1fea12..83c53d80a32f5f 100644
--- a/lib/internal/streams/pipeline.js
+++ b/lib/internal/streams/pipeline.js
@@ -225,6 +225,10 @@ function pipelineImpl(streams, callback, opts) {
     finishImpl(err, --finishCount === 0);
   }
 
+  function finishOnlyHandleError(err) {
+    finishImpl(err, false);
+  }
+
   function finishImpl(err, final) {
     if (err && (!error || error.code === 'ERR_STREAM_PREMATURE_CLOSE')) {
       error = err;
@@ -279,7 +283,7 @@ function pipelineImpl(streams, callback, opts) {
           err.name !== 'AbortError' &&
           err.code !== 'ERR_STREAM_PREMATURE_CLOSE'
         ) {
-          finish(err);
+          finishOnlyHandleError(err);
         }
       }
       stream.on('error', onError);
@@ -372,7 +376,7 @@ function pipelineImpl(streams, callback, opts) {
     } else if (isNodeStream(stream)) {
       if (isReadableNodeStream(ret)) {
         finishCount += 2;
-        const cleanup = pipe(ret, stream, finish, { end });
+        const cleanup = pipe(ret, stream, finish, finishOnlyHandleError, { end });
         if (isReadable(stream) && isLastStream) {
           lastStreamCleanup.push(cleanup);
         }
@@ -415,12 +419,12 @@ function pipelineImpl(streams, callback, opts) {
   return ret;
 }
 
-function pipe(src, dst, finish, { end }) {
+function pipe(src, dst, finish, finishOnlyHandleError, { end }) {
   let ended = false;
   dst.on('close', () => {
     if (!ended) {
       // Finish if the destination closes before the source has completed.
-      finish(new ERR_STREAM_PREMATURE_CLOSE());
+      finishOnlyHandleError(new ERR_STREAM_PREMATURE_CLOSE());
     }
   });
 
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index 7e69754b36d771..fc721c3a562b9e 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -1677,5 +1677,47 @@ tmpdir.refresh();
   pipeline(r, w, common.mustCall((err) => {
     assert.strictEqual(err, undefined);
   }));
+}
+
+{
+  // See https://github.com/nodejs/node/issues/51540 for the following 2 tests
+  const src = new Readable();
+  const dst = new Writable({
+    destroy(error, cb) {
+      // Takes a while to destroy
+      setImmediate(cb);
+    },
+  });
+
+  pipeline(src, dst, (err) => {
+    assert.strictEqual(src.closed, true);
+    assert.strictEqual(dst.closed, true);
+    assert.strictEqual(err.message, 'problem');
+  });
+  src.destroy(new Error('problem'));
+}
 
+{
+  const src = new Readable();
+  const dst = new Writable({
+    destroy(error, cb) {
+      // Takes a while to destroy
+      setImmediate(cb);
+    },
+  });
+  const passThroughs = [];
+  for (let i = 0; i < 10; i++) {
+    passThroughs.push(new PassThrough());
+  }
+
+  pipeline(src, ...passThroughs, dst, (err) => {
+    assert.strictEqual(src.closed, true);
+    assert.strictEqual(dst.closed, true);
+    assert.strictEqual(err.message, 'problem');
+
+    for (let i = 0; i < passThroughs.length; i++) {
+      assert.strictEqual(passThroughs[i].closed, true);
+    }
+  });
+  src.destroy(new Error('problem'));
 }