diff --git a/lib/internal/streams/pipeline.js b/lib/internal/streams/pipeline.js
index df0d7bc85d366c..94d5256c20095c 100644
--- a/lib/internal/streams/pipeline.js
+++ b/lib/internal/streams/pipeline.js
@@ -36,7 +36,7 @@ function destroyStream(stream, err) {
   if (typeof stream.close === 'function') return stream.close();
 }
 
-function destroyer(stream, reading, writing, callback) {
+function destroyer(stream, reading, writing, final, callback) {
   callback = once(callback);
   let destroyed = false;
 
@@ -44,7 +44,10 @@ function destroyer(stream, reading, writing, callback) {
   eos(stream, { readable: reading, writable: writing }, (err) => {
     if (destroyed) return;
     destroyed = true;
-    destroyStream(stream, err);
+    const readable = stream.readable || isRequest(stream);
+    if (err || !final || !readable) {
+      destroyStream(stream, err);
+    }
     callback(err);
   });
 
@@ -176,7 +179,7 @@ function pipeline(...streams) {
   }
 
   function wrap(stream, reading, writing, final) {
-    destroys.push(destroyer(stream, reading, writing, (err) => {
+    destroys.push(destroyer(stream, reading, writing, final, (err) => {
       finish(err, final);
     }));
   }
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index 6bfa1331834968..0d90f65f5a6643 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -918,6 +918,52 @@ const { promisify } = require('util');
   const dst = new PassThrough({ autoDestroy: false });
   pipeline(src, dst, common.mustCall(() => {
     assert.strictEqual(src.destroyed, true);
+    assert.strictEqual(dst.destroyed, false);
+  }));
+  src.end();
+}
+
+{
+  const server = http.createServer((req, res) => {
+  });
+
+  server.listen(0, () => {
+    const req = http.request({
+      port: server.address().port
+    });
+
+    const body = new PassThrough();
+    pipeline(
+      body,
+      req,
+      common.mustCall((err) => {
+        assert(!err);
+        assert(!req.res);
+        assert(!req.aborted);
+        req.abort();
+        server.close();
+      })
+    );
+    body.end();
+  });
+}
+
+{
+  const src = new PassThrough();
+  const dst = new PassThrough();
+  pipeline(src, dst, common.mustCall((err) => {
+    assert(!err);
+    assert.strictEqual(dst.destroyed, false);
+  }));
+  src.end();
+}
+
+{
+  const src = new PassThrough();
+  const dst = new PassThrough();
+  dst.readable = false;
+  pipeline(src, dst, common.mustCall((err) => {
+    assert(!err);
     assert.strictEqual(dst.destroyed, true);
   }));
   src.end();