diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 8f11e5db2ab7d4..69845a3f900219 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -494,7 +494,7 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
               dest !== process.stdout &&
               dest !== process.stderr;
 
-  var endFn = doEnd ? onend : cleanup;
+  var endFn = doEnd ? onend : unpipe;
   if (state.endEmitted)
     process.nextTick(endFn);
   else
@@ -530,7 +530,7 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
     dest.removeListener('error', onerror);
     dest.removeListener('unpipe', onunpipe);
     src.removeListener('end', onend);
-    src.removeListener('end', cleanup);
+    src.removeListener('end', unpipe);
     src.removeListener('data', ondata);
 
     cleanedUp = true;
diff --git a/test/parallel/test-stream-unpipe-event.js b/test/parallel/test-stream-unpipe-event.js
new file mode 100644
index 00000000000000..a9e634a11a3092
--- /dev/null
+++ b/test/parallel/test-stream-unpipe-event.js
@@ -0,0 +1,87 @@
+'use strict';
+const common = require('../common');
+const assert = require('assert');
+const {Writable, Readable} = require('stream');
+class NullWriteable extends Writable {
+  _write(chunk, encoding, callback) {
+    return callback();
+  }
+}
+class QuickEndReadable extends Readable {
+  _read() {
+    this.push(null);
+  }
+}
+class NeverEndReadable extends Readable {
+  _read() {}
+}
+
+function noop() {}
+
+{
+  const dest = new NullWriteable();
+  const src = new QuickEndReadable();
+  dest.on('pipe', common.mustCall(noop));
+  dest.on('unpipe', common.mustCall(noop));
+  src.pipe(dest);
+  setImmediate(() => {
+    assert.strictEqual(src._readableState.pipesCount, 0);
+  });
+}
+
+{
+  const dest = new NullWriteable();
+  const src = new NeverEndReadable();
+  dest.on('pipe', common.mustCall(noop));
+  dest.on('unpipe', common.mustNotCall('unpipe should not have been emitted'));
+  src.pipe(dest);
+  setImmediate(() => {
+    assert.strictEqual(src._readableState.pipesCount, 1);
+  });
+}
+
+{
+  const dest = new NullWriteable();
+  const src = new NeverEndReadable();
+  dest.on('pipe', common.mustCall(noop));
+  dest.on('unpipe', common.mustCall(noop));
+  src.pipe(dest);
+  src.unpipe(dest);
+  setImmediate(() => {
+    assert.strictEqual(src._readableState.pipesCount, 0);
+  });
+}
+
+{
+  const dest = new NullWriteable();
+  const src = new QuickEndReadable();
+  dest.on('pipe', common.mustCall(noop));
+  dest.on('unpipe', common.mustCall(noop));
+  src.pipe(dest, {end: false});
+  setImmediate(() => {
+    assert.strictEqual(src._readableState.pipesCount, 0);
+  });
+}
+
+{
+  const dest = new NullWriteable();
+  const src = new NeverEndReadable();
+  dest.on('pipe', common.mustCall(noop));
+  dest.on('unpipe', common.mustNotCall('unpipe should not have been emitted'));
+  src.pipe(dest, {end: false});
+  setImmediate(() => {
+    assert.strictEqual(src._readableState.pipesCount, 1);
+  });
+}
+
+{
+  const dest = new NullWriteable();
+  const src = new NeverEndReadable();
+  dest.on('pipe', common.mustCall(noop));
+  dest.on('unpipe', common.mustCall(noop));
+  src.pipe(dest, {end: false});
+  src.unpipe(dest);
+  setImmediate(() => {
+    assert.strictEqual(src._readableState.pipesCount, 0);
+  });
+}