diff --git a/doc/api/stream.md b/doc/api/stream.md
index a6f35dc9c0..1eb137ef9c 100644
--- a/doc/api/stream.md
+++ b/doc/api/stream.md
@@ -1559,7 +1559,9 @@ Because JavaScript does not have support for multiple inheritance, the
 to extending the `stream.Readable` *and* `stream.Writable` classes).
 
 *Note*: The `stream.Duplex` class prototypically inherits from `stream.Readable`
-and parasitically from `stream.Writable`.
+and parasitically from `stream.Writable`, but `instanceof` will work properly
+for both base classes due to overriding [`Symbol.hasInstance`][]
+on `stream.Writable`.
 
 Custom Duplex streams *must* call the `new stream.Duplex([options])`
 constructor and implement *both* the `readable._read()` and
@@ -2009,3 +2011,4 @@ readable buffer so there is nothing for a user to consume.
 [Transform]: #stream_class_stream_transform
 [Writable]: #stream_class_stream_writable
 [zlib]: zlib.html
+[`Symbol.hasInstance`]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Symbol/hasInstance
diff --git a/lib/_stream_writable.js b/lib/_stream_writable.js
index 88c19cddbf..c0264df04b 100644
--- a/lib/_stream_writable.js
+++ b/lib/_stream_writable.js
@@ -134,11 +134,32 @@ Object.defineProperty(WritableState.prototype, 'buffer', {
      'instead.')
 });
 
+// Test _writableState for inheritance to account for Duplex streams,
+// whose prototype chain only points to Readable.
+var realHasInstance;
+if (typeof Symbol === 'function' && Symbol.hasInstance) {
+  realHasInstance = Function.prototype[Symbol.hasInstance];
+  Object.defineProperty(Writable, Symbol.hasInstance, {
+    value: function(object) {
+      // Trying to move the `realHasInstance` from the Writable constructor
+      // to here will break the Node.js LazyTransform implementation.
+      return object._writableState instanceof WritableState;
+    }
+  });
+} else {
+  realHasInstance = function(object) {
+    return object instanceof this;
+  };
+}
+
 function Writable(options) {
-  // Writable ctor is applied to Duplexes, though they're not
-  // instanceof Writable, they're instanceof Readable.
-  if (!(this instanceof Writable) && !(this instanceof Stream.Duplex))
+  // Writable ctor is applied to Duplexes, too.
+  // `realHasInstance` is necessary because using plain `instanceof`
+  // would return false, as no `_writableState` property is attached.
+  if (!(realHasInstance.call(Writable, this)) &&
+      !(this instanceof Stream.Duplex)) {
     return new Writable(options);
+  }
 
   this._writableState = new WritableState(options, this);
 
diff --git a/test/parallel/test-stream-inheritance.js b/test/parallel/test-stream-inheritance.js
new file mode 100644
index 0000000000..efc28731bd
--- /dev/null
+++ b/test/parallel/test-stream-inheritance.js
@@ -0,0 +1,29 @@
+'use strict';
+require('../common');
+const assert = require('assert');
+const { Readable, Writable, Duplex, Transform } = require('stream');
+
+const readable = new Readable({ read() {} });
+const writable = new Writable({ write() {} });
+const duplex = new Duplex({ read() {}, write() {} });
+const transform = new Transform({ transform() {} });
+
+assert.ok(readable instanceof Readable);
+assert.ok(!(writable instanceof Readable));
+assert.ok(duplex instanceof Readable);
+assert.ok(transform instanceof Readable);
+
+assert.ok(!(readable instanceof Writable));
+assert.ok(writable instanceof Writable);
+assert.ok(duplex instanceof Writable);
+assert.ok(transform instanceof Writable);
+
+assert.ok(!(readable instanceof Duplex));
+assert.ok(!(writable instanceof Duplex));
+assert.ok(duplex instanceof Duplex);
+assert.ok(transform instanceof Duplex);
+
+assert.ok(!(readable instanceof Transform));
+assert.ok(!(writable instanceof Transform));
+assert.ok(!(duplex instanceof Transform));
+assert.ok(transform instanceof Transform);