diff --git a/lib/internal/streams/end-of-stream.js b/lib/internal/streams/end-of-stream.js
index aad43823f9afb9..6e590401f1e56e 100644
--- a/lib/internal/streams/end-of-stream.js
+++ b/lib/internal/streams/end-of-stream.js
@@ -63,15 +63,33 @@ function eos(stream, opts, callback) {
 
   const wState = stream._writableState;
   const rState = stream._readableState;
+  const state = wState || rState;
 
   const onlegacyfinish = () => {
     if (!stream.writable) onfinish();
   };
 
+  // TODO (ronag): Improve soft detection to include core modules and
+  // common ecosystem modules that do properly emit 'close' but fail
+  // this generic check.
+  const willEmitClose = (
+    state &&
+    state.autoDestroy &&
+    state.emitClose &&
+    state.closed === false
+  );
+
   let writableFinished = stream.writableFinished ||
     (wState && wState.finished);
   const onfinish = () => {
     writableFinished = true;
+    if (willEmitClose && (!stream.readable || readable)) {
+      // TODO(ronag): Duplex won't autoDestroy if `stream.readable` was
+      // explicitly set to false.
+      if (!rState || rState.readable !== false) {
+        return;
+      }
+    }
     if (!readable || readableEnded) callback.call(stream);
   };
 
@@ -79,6 +97,13 @@ function eos(stream, opts, callback) {
     (rState && rState.endEmitted);
   const onend = () => {
     readableEnded = true;
+    if (willEmitClose && (!stream.writable || writable)) {
+      // TODO(ronag): Duplex won't autoDestroy if `stream.writable` was
+      // explicitly set to false.
+      if (!wState || wState.writable !== false) {
+        return;
+      }
+    }
     if (!writable || writableFinished) callback.call(stream);
   };
 
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index c2b454e80b38af..b273fddfa3b613 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -7,7 +7,8 @@ const {
   Readable,
   Transform,
   pipeline,
-  PassThrough
+  PassThrough,
+  Duplex
 } = require('stream');
 const assert = require('assert');
 const http = require('http');
@@ -1077,3 +1078,43 @@ const { promisify } = require('util');
     assert.ifError(err);
   }));
 }
+
+{
+  let closed = false;
+  const src = new Readable({
+    read() {},
+    destroy(err, cb) {
+      process.nextTick(cb);
+    }
+  });
+  const dst = new Writable({
+    write(chunk, encoding, callback) {
+      callback();
+    }
+  });
+  src.on('close', () => {
+    closed = true;
+  });
+  src.push(null);
+  pipeline(src, dst, common.mustCall((err) => {
+    assert.strictEqual(closed, true);
+  }));
+}
+
+{
+  let closed = false;
+  const src = new Readable({
+    read() {},
+    destroy(err, cb) {
+      process.nextTick(cb);
+    }
+  });
+  const dst = new Duplex({});
+  src.on('close', common.mustCall(() => {
+    closed = true;
+  }));
+  src.push(null);
+  pipeline(src, dst, common.mustCall((err) => {
+    assert.strictEqual(closed, true);
+  }));
+}