diff --git a/lib/internal/streams/end-of-stream.js b/lib/internal/streams/end-of-stream.js
index 8bbd4827b23a3a..4ad7b93337f633 100644
--- a/lib/internal/streams/end-of-stream.js
+++ b/lib/internal/streams/end-of-stream.js
@@ -36,8 +36,6 @@ function eos(stream, opts, callback) {
 
   callback = once(callback);
 
-  const ws = stream._writableState;
-  const rs = stream._readableState;
   let readable = opts.readable || (opts.readable !== false && stream.readable);
   let writable = opts.writable || (opts.writable !== false && stream.writable);
 
@@ -45,13 +43,17 @@ function eos(stream, opts, callback) {
     if (!stream.writable) onfinish();
   };
 
+  var writableEnded = stream._writableState && stream._writableState.finished;
   const onfinish = () => {
     writable = false;
+    writableEnded = true;
     if (!readable) callback.call(stream);
   };
 
+  var readableEnded = stream._readableState && stream._readableState.endEmitted;
   const onend = () => {
     readable = false;
+    readableEnded = true;
     if (!writable) callback.call(stream);
   };
 
@@ -60,11 +62,16 @@ function eos(stream, opts, callback) {
   };
 
   const onclose = () => {
-    if (readable && !(rs && rs.ended)) {
-      return callback.call(stream, new ERR_STREAM_PREMATURE_CLOSE());
+    let err;
+    if (readable && !readableEnded) {
+      if (!stream._readableState || !stream._readableState.ended)
+        err = new ERR_STREAM_PREMATURE_CLOSE();
+      return callback.call(stream, err);
     }
-    if (writable && !(ws && ws.ended)) {
-      return callback.call(stream, new ERR_STREAM_PREMATURE_CLOSE());
+    if (writable && !writableEnded) {
+      if (!stream._writableState || !stream._writableState.ended)
+        err = new ERR_STREAM_PREMATURE_CLOSE();
+      return callback.call(stream, err);
     }
   };
 
@@ -77,7 +84,7 @@ function eos(stream, opts, callback) {
     stream.on('abort', onclose);
     if (stream.req) onrequest();
     else stream.on('request', onrequest);
-  } else if (writable && !ws) { // legacy streams
+  } else if (writable && !stream._writableState) { // legacy streams
     stream.on('end', onlegacyfinish);
     stream.on('close', onlegacyfinish);
   }
diff --git a/test/parallel/parallel.status b/test/parallel/parallel.status
index cfc4e36e9a565f..b45e4448d97c06 100644
--- a/test/parallel/parallel.status
+++ b/test/parallel/parallel.status
@@ -12,8 +12,6 @@ test-net-connect-options-port: PASS,FLAKY
 test-http2-pipe: PASS,FLAKY
 test-worker-syntax-error: PASS,FLAKY
 test-worker-syntax-error-file: PASS,FLAKY
-# https://github.com/nodejs/node/issues/24456
-test-stream-pipeline-http2: PASS,FLAKY
 
 [$system==linux]
 
diff --git a/test/parallel/test-stream-pipeline-queued-end-in-destroy.js b/test/parallel/test-stream-pipeline-queued-end-in-destroy.js
new file mode 100644
index 00000000000000..d5e399ddda531b
--- /dev/null
+++ b/test/parallel/test-stream-pipeline-queued-end-in-destroy.js
@@ -0,0 +1,39 @@
+'use strict';
+const common = require('../common');
+const assert = require('assert');
+const { Readable, Duplex, pipeline } = require('stream');
+
+// Test that the callback for pipeline() is called even when the ._destroy()
+// method of the stream places an .end() request to itself that does not
+// get processed before the destruction of the stream (i.e. the 'close' event).
+// Refs: https://github.com/nodejs/node/issues/24456
+
+const readable = new Readable({
+  read: common.mustCall(() => {})
+});
+
+const duplex = new Duplex({
+  write(chunk, enc, cb) {
+    // Simulate messages queueing up.
+  },
+  read() {},
+  destroy(err, cb) {
+    // Call end() from inside the destroy() method, like HTTP/2 streams
+    // do at the time of writing.
+    this.end();
+    cb(err);
+  }
+});
+
+duplex.on('finished', common.mustNotCall());
+
+pipeline(readable, duplex, common.mustCall((err) => {
+  assert.strictEqual(err.code, 'ERR_STREAM_PREMATURE_CLOSE');
+}));
+
+// Write one chunk of data, and destroy the stream later.
+// That should trigger the pipeline destruction.
+readable.push('foo');
+setImmediate(() => {
+  readable.destroy();
+});