diff --git a/lib/internal/streams/end-of-stream.js b/lib/internal/streams/end-of-stream.js
index 88bdcb643dd201..9f1e0ba0dc93f2 100644
--- a/lib/internal/streams/end-of-stream.js
+++ b/lib/internal/streams/end-of-stream.js
@@ -34,6 +34,13 @@ function isWritableFinished(stream) {
 
 function nop() {}
 
+function isReadableEnded(stream) {
+  if (stream.readableEnded) return true;
+  const rState = stream._readableState;
+  if (!rState || rState.errored) return false;
+  return rState.endEmitted || (rState.ended && rState.length === 0);
+}
+
 function eos(stream, opts, callback) {
   if (arguments.length === 2) {
     callback = opts;
@@ -84,7 +91,7 @@ function eos(stream, opts, callback) {
   const onclose = () => {
     let err;
     if (readable && !readableEnded) {
-      if (!rState || !rState.ended)
+      if (!isReadableEnded(stream))
         err = new ERR_STREAM_PREMATURE_CLOSE();
       return callback.call(stream, err);
     }
diff --git a/lib/internal/streams/pipeline.js b/lib/internal/streams/pipeline.js
index 8c6cbf7524ea53..46d499709ee45e 100644
--- a/lib/internal/streams/pipeline.js
+++ b/lib/internal/streams/pipeline.js
@@ -26,23 +26,37 @@ let PassThrough;
 let createReadableStreamAsyncIterator;
 
 function destroyer(stream, reading, writing, callback) {
-  callback = once(callback);
-  let destroyed = false;
+  const _destroy = once((err) => {
+    destroyImpl.destroyer(stream, err);
+    callback(err);
+  });
 
   if (eos === undefined) eos = require('internal/streams/end-of-stream');
   eos(stream, { readable: reading, writable: writing }, (err) => {
-    if (destroyed) return;
-    destroyed = true;
-    destroyImpl.destroyer(stream, err);
-    callback(err);
+    const rState = stream._readableState;
+    if (
+      err &&
+      err.code === 'ERR_STREAM_PREMATURE_CLOSE' &&
+      reading &&
+      (rState && rState.ended && !rState.errored && !rState.errorEmitted)
+    ) {
+      // Some readable streams will emit 'close' before 'end'. However, since
+      // this is on the readable side 'end' should still be emitted if the
+      // stream has been ended and no error emitted. This should be allowed in
+      // favor of backwards compatibility. Since the stream is piped to a
+      // destination this should not result in any observable difference.
+      // We don't need to check if this is a writable premature close since
+      // eos will only fail with premature close on the reading side for
+      // duplex streams.
+      stream
+        .once('end', _destroy)
+        .once('error', _destroy);
+    } else {
+      _destroy(err);
+    }
   });
 
-  return (err) => {
-    if (destroyed) return;
-    destroyed = true;
-    destroyImpl.destroyer(stream, err);
-    callback(err || new ERR_STREAM_DESTROYED('pipe'));
-  };
+  return (err) => _destroy(err || new ERR_STREAM_DESTROYED('pipe'));
 }
 
 function popCallback(streams) {
diff --git a/test/parallel/test-stream-finished.js b/test/parallel/test-stream-finished.js
index c9c6bafd642e97..46a5f93913418b 100644
--- a/test/parallel/test-stream-finished.js
+++ b/test/parallel/test-stream-finished.js
@@ -342,3 +342,13 @@ testClosed((opts) => new Writable({ write() {}, ...opts }));
   d._writableState.errored = true;
   d.emit('close');
 }
+
+{
+  const r = new Readable();
+  finished(r, common.mustCall((err) => {
+    assert.strictEqual(err.code, 'ERR_STREAM_PREMATURE_CLOSE');
+  }));
+  r.push('asd');
+  r.push(null);
+  r.destroy();
+}
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index 87e11f8116204e..74473b0db40600 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -920,3 +920,21 @@ const { promisify } = require('util');
   }));
   src.end();
 }
+
+{
+  // Make sure 'close' before 'end' finishes without error
+  // if readable has received eof.
+  // Ref: https://github.com/nodejs/node/issues/29699
+  const r = new Readable();
+  const w = new Writable({
+    write(chunk, encoding, cb) {
+      cb();
+    }
+  });
+  pipeline(r, w, (err) => {
+    assert.strictEqual(err, undefined);
+  });
+  r.push('asd');
+  r.push(null);
+  r.emit('close');
+}