diff --git a/doc/api/stream.md b/doc/api/stream.md
index cf03163218bfbc..b2f121f62604e0 100644
--- a/doc/api/stream.md
+++ b/doc/api/stream.md
@@ -1525,6 +1525,11 @@ Especially useful in error handling scenarios where a stream is destroyed
 prematurely (like an aborted HTTP request), and will not emit `'end'`
 or `'finish'`.
 
+`stream.finished()` will error with `ERR_STREAM_PREMATURE_CLOSE` if:
+* `Writable` emits `'close'` before `'finish'` and
+[`writable.writableFinished`][].
+* `Readable` emits `'close'` before `'end'` and [`readable.readableEnded`][].
+
 The `finished` API is promisify-able as well;
 
 ```js
@@ -1647,6 +1652,10 @@ run().catch(console.error);
 * `Readable` streams which have emitted `'end'` or `'close'`.
 * `Writable` streams which have emitted `'finish'` or `'close'`.
 
+If any `Writable` or `Readable` stream emits `'close'` without being able to
+fully flush or drain, `stream.pipeline()` will error with
+`ERR_STREAM_PREMATURE_CLOSE`.
+
 `stream.pipeline()` leaves dangling event listeners on the streams
 after the `callback` has been invoked. In the case of reuse of streams after
 failure, this can cause event listener leaks and swallowed errors.
@@ -2865,6 +2874,7 @@ contain multi-byte characters.
 [`process.stdout`]: process.html#process_process_stdout
 [`readable._read()`]: #stream_readable_read_size_1
 [`readable.push('')`]: #stream_readable_push
+[`readable.readableEnded`]: #stream_readable_readableended
 [`readable.setEncoding()`]: #stream_readable_setencoding_encoding
 [`stream.Readable.from()`]: #stream_stream_readable_from_iterable_options
 [`stream.cork()`]: #stream_writable_cork
diff --git a/lib/internal/streams/end-of-stream.js b/lib/internal/streams/end-of-stream.js
index 585a52ae2f2382..dd42eb9f5b3f46 100644
--- a/lib/internal/streams/end-of-stream.js
+++ b/lib/internal/streams/end-of-stream.js
@@ -79,10 +79,24 @@ function eos(stream, opts, callback) {
   };
 
   const onclose = () => {
-    if (readable && !readableEnded) {
-      callback.call(stream, new ERR_STREAM_PREMATURE_CLOSE());
-    } else if (writable && !writableFinished) {
-      callback.call(stream, new ERR_STREAM_PREMATURE_CLOSE());
+    if (readable) {
+      const ended = (stream._readableState &&
+        stream._readableState.endEmitted) || stream.readableEnded;
+      if (!ended && !readableEnded) {
+        callback.call(stream, new ERR_STREAM_PREMATURE_CLOSE());
+      } else if (!readableEnded) {
+        // Compat. Stream has ended but haven't emitted 'end'.
+        callback.call(stream);
+      }
+    } else if (writable) {
+      const finished = (stream._writableState &&
+        stream._writableState.finished) || stream.writableFinished;
+      if (!finished && !writableFinished) {
+        callback.call(stream, new ERR_STREAM_PREMATURE_CLOSE());
+      } else if (!writableFinished) {
+        // Compat. Stream has finished but haven't emitted 'finish'.
+        callback.call(stream);
+      }
     }
   };
 
diff --git a/lib/internal/streams/pipeline.js b/lib/internal/streams/pipeline.js
index e0834171bfb8fc..9a3521f523b54e 100644
--- a/lib/internal/streams/pipeline.js
+++ b/lib/internal/streams/pipeline.js
@@ -46,6 +46,29 @@ function destroyer(stream, reading, writing, callback) {
 
   if (eos === undefined) eos = require('internal/streams/end-of-stream');
   eos(stream, { readable: reading, writable: writing }, (err) => {
+    if (
+      err &&
+      err.code === 'ERR_STREAM_PREMATURE_CLOSE' &&
+      reading &&
+      (stream._readableState && stream._readableState.ended)
+    ) {
+      // 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
+        .on('end', () => {
+          closed = true;
+          callback();
+        })
+        .on('error', callback);
+      return;
+    }
+
     if (err) return callback(err);
     closed = true;
     callback();
diff --git a/test/parallel/test-http-client-finished.js b/test/parallel/test-http-client-finished.js
index 337f7b596d7442..8eddf8660b4476 100644
--- a/test/parallel/test-http-client-finished.js
+++ b/test/parallel/test-http-client-finished.js
@@ -55,7 +55,7 @@ const { finished } = require('stream');
     }).end();
     finished(req, (err) => {
       common.expectsError({
-        type: Error,
+        name: 'Error',
         code: 'ERR_STREAM_PREMATURE_CLOSE'
       })(err);
       finished(req, common.mustCall(() => {
diff --git a/test/parallel/test-stream-finished.js b/test/parallel/test-stream-finished.js
index c5e792b45e2e4b..caca55601868a2 100644
--- a/test/parallel/test-stream-finished.js
+++ b/test/parallel/test-stream-finished.js
@@ -273,27 +273,26 @@ const { promisify } = require('util');
 }
 
 {
-  // Premature close if stream never emitted 'finish'
-  // even if writableFinished says something else.
+  // No error if stream never emitted 'end'
+  // even if readableEnded says something else.
 
   const streamLike = new EE();
   streamLike.writable = true;
-  finished(streamLike, common.expectsError({
-    code: 'ERR_STREAM_PREMATURE_CLOSE'
+  finished(streamLike, common.mustCall((err) => {
+    assert.strictEqual(err, undefined);
   }));
   streamLike.writableFinished = true;
   streamLike.emit('close');
 }
 
-
 {
-  // Premature close if stream never emitted 'end'
-  // even if readableEnded says something else.
+  // No error if stream never emitted 'finished'
+  // even if writableFinished says something else.
 
   const streamLike = new EE();
   streamLike.readable = true;
-  finished(streamLike, common.expectsError({
-    code: 'ERR_STREAM_PREMATURE_CLOSE'
+  finished(streamLike, common.mustCall((err) => {
+    assert.strictEqual(err, undefined);
   }));
   streamLike.readableEnded = true;
   streamLike.emit('close');
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index 19fc246e2bf3cd..99876738415c69 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -912,4 +912,35 @@ const { promisify } = require('util');
   }, common.mustCall((err) => {
     assert.strictEqual(err.message, 'kaboom');
   }));
+  // 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(null);
+  r.destroy();
+}
+
+{
+  // 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(null);
+  r.emit('close');
 }