diff --git a/lib/internal/streams/pipeline.js b/lib/internal/streams/pipeline.js
index 44c0e06ee30557..ee342f8861d5bc 100644
--- a/lib/internal/streams/pipeline.js
+++ b/lib/internal/streams/pipeline.js
@@ -38,6 +38,7 @@ const {
   isTransformStream,
   isWebStream,
   isReadableStream,
+  isReadableFinished,
 } = require('internal/streams/utils');
 const { AbortController } = require('internal/abort_controller');
 
@@ -417,10 +418,17 @@ function pipe(src, dst, finish, { end }) {
     // Compat. Before node v10.12.0 stdio used to throw an error so
     // pipe() did/does not end() stdio destinations.
     // Now they allow it but "secretly" don't close the underlying fd.
-    src.once('end', () => {
+
+    function endFn() {
       ended = true;
       dst.end();
-    });
+    }
+
+    src.once('end', endFn);
+
+    if (isReadableFinished(src)) { // End the destination if the source has already ended.
+      process.nextTick(endFn);
+    }
   } else {
     finish();
   }
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index 65ef5164c14b4c..d37ca275f1dddf 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -1591,3 +1591,28 @@ const tsp = require('timers/promises');
     assert.strictEqual(writable.endCount, 1);
   }));
 }
+
+{
+  const readable = new Readable({
+    read() {}
+  });
+  readable.on('end', common.mustCall(() => {
+    pipeline(readable, new PassThrough(), common.mustSucceed());
+  }));
+  readable.push(null);
+  readable.read();
+}
+
+{
+  const dup = new Duplex({
+    read() {},
+    write(chunk, enc, cb) {
+      cb();
+    }
+  });
+  dup.on('end', common.mustCall(() => {
+    pipeline(dup, new PassThrough(), common.mustSucceed());
+  }));
+  dup.push(null);
+  dup.read();
+}
diff --git a/test/parallel/test-webstreams-pipeline.js b/test/parallel/test-webstreams-pipeline.js
index 46bdf8718ea97a..ac673dd9d42ea7 100644
--- a/test/parallel/test-webstreams-pipeline.js
+++ b/test/parallel/test-webstreams-pipeline.js
@@ -2,7 +2,7 @@
 
 const common = require('../common');
 const assert = require('assert');
-const { Readable, Writable, Transform, pipeline } = require('stream');
+const { Readable, Writable, Transform, pipeline, PassThrough } = require('stream');
 const { pipeline: pipelinePromise } = require('stream/promises');
 const { ReadableStream, WritableStream, TransformStream } = require('stream/web');
 const http = require('http');
@@ -410,3 +410,13 @@ const http = require('http');
   }
   c.close();
 }
+
+{
+  const rs = new ReadableStream({
+    start(controller) {
+      controller.close();
+    }
+  });
+
+  pipeline(rs, new PassThrough(), common.mustSucceed());
+}