diff --git a/lib/_http_client.js b/lib/_http_client.js
index f3b88b62730175..fde7fde86bbf25 100644
--- a/lib/_http_client.js
+++ b/lib/_http_client.js
@@ -53,6 +53,7 @@ const {
   prepareError,
 } = require('_http_common');
 const { OutgoingMessage } = require('_http_outgoing');
+const { kDestroy } = require('internal/streams/destroy');
 const Agent = require('_http_agent');
 const { Buffer } = require('buffer');
 const { defaultTriggerAsyncIdScope } = require('internal/async_hooks');
@@ -609,6 +610,7 @@ function parserOnIncomingClient(res, shouldKeepAlive) {
   DTRACE_HTTP_CLIENT_RESPONSE(socket, req);
   req.res = res;
   res.req = req;
+  res[kDestroy] = null;
 
   // Add our listener first, so that we guarantee socket cleanup
   res.on('end', responseOnEnd);
diff --git a/lib/_http_incoming.js b/lib/_http_incoming.js
index e0f1354e6c969c..3961b583de9ddc 100644
--- a/lib/_http_incoming.js
+++ b/lib/_http_incoming.js
@@ -31,6 +31,7 @@ const {
 } = primordials;
 
 const { Readable, finished } = require('stream');
+const { kDestroy } = require('internal/streams/destroy');
 
 const kHeaders = Symbol('kHeaders');
 const kHeadersCount = Symbol('kHeadersCount');
@@ -188,13 +189,18 @@ IncomingMessage.prototype._destroy = function _destroy(err, cb) {
     this.socket.destroy(err);
     const cleanup = finished(this.socket, (e) => {
       cleanup();
-      onError(this, e || err, cb);
+      process.nextTick(onError, this, e || err, cb);
     });
   } else {
-    onError(this, err, cb);
+    process.nextTick(onError, this, err, cb);
   }
 };
 
+IncomingMessage.prototype[kDestroy] = function(err) {
+  this.socket = null;
+  this.destroy(err);
+};
+
 IncomingMessage.prototype._addHeaderLines = _addHeaderLines;
 function _addHeaderLines(headers, n) {
   if (headers && headers.length) {
diff --git a/lib/_http_server.js b/lib/_http_server.js
index 97df58a007daba..946394f9add754 100644
--- a/lib/_http_server.js
+++ b/lib/_http_server.js
@@ -231,9 +231,7 @@ function onServerResponseClose() {
   // where the ServerResponse object has already been deconstructed.
   // Fortunately, that requires only a single if check. :-)
   if (this._httpMessage) {
-    this._httpMessage.destroyed = true;
-    this._httpMessage._closed = true;
-    this._httpMessage.emit('close');
+    emitCloseNT(this._httpMessage);
   }
 }
 
@@ -837,9 +835,11 @@ function resOnFinish(req, res, socket, state, server) {
 }
 
 function emitCloseNT(self) {
-  self.destroyed = true;
-  self._closed = true;
-  self.emit('close');
+  if (!self.destroyed) {
+    self.destroyed = true;
+    self._closed = true;
+    self.emit('close');
+  }
 }
 
 // The following callback is issued after the headers have been read on a
diff --git a/lib/internal/streams/destroy.js b/lib/internal/streams/destroy.js
index a2892c67a0fcfa..4238e12074d769 100644
--- a/lib/internal/streams/destroy.js
+++ b/lib/internal/streams/destroy.js
@@ -5,6 +5,7 @@ const {
   codes: {
     ERR_MULTIPLE_CALLBACK,
   },
+  AbortError,
 } = require('internal/errors');
 const {
   Symbol,
@@ -363,15 +364,65 @@ function isRequest(stream) {
   return stream && stream.setHeader && typeof stream.abort === 'function';
 }
 
+const kDestroyed = Symbol('kDestroyed');
+
+function emitCloseLegacy(stream) {
+  stream.emit('close');
+}
+
+function emitErrorCloseLegacy(stream, err) {
+  stream.emit('error', err);
+  process.nextTick(emitCloseLegacy, stream);
+}
+
+function isDestroyed(stream) {
+  return stream.destroyed || stream[kDestroyed];
+}
+
+function isReadable(stream) {
+  return stream.readable && !stream.readableEnded && !isDestroyed(stream);
+}
+
+function isWritable(stream) {
+  return stream.writable && !stream.writableEnded && !isDestroyed(stream);
+}
+
 // Normalize destroy for legacy.
 function destroyer(stream, err) {
-  if (isRequest(stream)) return stream.abort();
-  if (isRequest(stream.req)) return stream.req.abort();
-  if (typeof stream.destroy === 'function') return stream.destroy(err);
-  if (typeof stream.close === 'function') return stream.close();
+  if (isDestroyed(stream)) {
+    return;
+  }
+
+  if (!err && (isReadable(stream) || isWritable(stream))) {
+    err = new AbortError();
+  }
+
+  // TODO: Remove isRequest branches.
+  if (typeof stream[kDestroy] === 'function') {
+    stream[kDestroy](err);
+  } else if (isRequest(stream)) {
+    stream.abort();
+  } else if (isRequest(stream.req)) {
+    stream.req.abort();
+  } else if (typeof stream.destroy === 'function') {
+    stream.destroy(err);
+  } else if (typeof stream.close === 'function') {
+    // TODO: Don't lose err?
+    stream.close();
+  } else if (err) {
+    process.nextTick(emitErrorCloseLegacy, stream);
+  } else {
+    process.nextTick(emitCloseLegacy, stream);
+  }
+
+  if (!stream.destroyed) {
+    stream[kDestroyed] = true;
+  }
 }
 
 module.exports = {
+  kDestroy,
+  isDestroyed,
   construct,
   destroyer,
   destroy,
diff --git a/lib/stream.js b/lib/stream.js
index 85adda81b32f29..16a2370232e360 100644
--- a/lib/stream.js
+++ b/lib/stream.js
@@ -30,6 +30,7 @@ const {
 } = require('internal/util');
 
 const pipeline = require('internal/streams/pipeline');
+const { destroyer } = require('internal/streams/destroy');
 const eos = require('internal/streams/end-of-stream');
 const internalBuffer = require('internal/buffer');
 
@@ -45,6 +46,7 @@ Stream.pipeline = pipeline;
 const { addAbortSignal } = require('internal/streams/add-abort-signal');
 Stream.addAbortSignal = addAbortSignal;
 Stream.finished = eos;
+Stream.destroy = destroyer;
 
 ObjectDefineProperty(Stream, 'promises', {
   configurable: true,
diff --git a/test/parallel/test-stream-destroy.js b/test/parallel/test-stream-destroy.js
new file mode 100644
index 00000000000000..f99c29c811932d
--- /dev/null
+++ b/test/parallel/test-stream-destroy.js
@@ -0,0 +1,115 @@
+'use strict';
+
+const common = require('../common');
+const {
+  Writable,
+  Readable,
+  destroy
+} = require('stream');
+const assert = require('assert');
+const http = require('http');
+
+{
+  const r = new Readable({ read() {} });
+  destroy(r);
+  assert.strictEqual(r.destroyed, true);
+  r.on('error', common.mustCall((err) => {
+    assert.strictEqual(err.name, 'AbortError');
+  }));
+  r.on('close', common.mustCall());
+}
+
+{
+  const r = new Readable({ read() {} });
+  destroy(r, new Error('asd'));
+  assert.strictEqual(r.destroyed, true);
+  r.on('error', common.mustCall((err) => {
+    assert.strictEqual(err.message, 'asd');
+  }));
+  r.on('close', common.mustCall());
+}
+
+{
+  const w = new Writable({ write() {} });
+  destroy(w);
+  assert.strictEqual(w.destroyed, true);
+  w.on('error', common.mustCall((err) => {
+    assert.strictEqual(err.name, 'AbortError');
+  }));
+  w.on('close', common.mustCall());
+}
+
+{
+  const w = new Writable({ write() {} });
+  destroy(w, new Error('asd'));
+  assert.strictEqual(w.destroyed, true);
+  w.on('error', common.mustCall((err) => {
+    assert.strictEqual(err.message, 'asd');
+  }));
+  w.on('close', common.mustCall());
+}
+
+{
+  const server = http.createServer((req, res) => {
+    destroy(req);
+    req.on('error', common.mustCall((err) => {
+      assert.strictEqual(err.name, 'AbortError');
+    }));
+    req.on('close', common.mustCall(() => {
+      res.end('hello');
+    }));
+  });
+
+  server.listen(0, () => {
+    const req = http.request({
+      port: server.address().port
+    });
+
+    req.write('asd');
+    req.on('response', (res) => {
+      const buf = [];
+      res.on('data', (data) => buf.push(data));
+      res.on('end', common.mustCall(() => {
+        assert.deepStrictEqual(
+          Buffer.concat(buf),
+          Buffer.from('hello')
+        );
+        server.close();
+      }));
+    });
+  });
+}
+
+{
+  const server = http.createServer((req, res) => {
+    req
+      .resume()
+      .on('end', () => {
+        destroy(req);
+      })
+      .on('error', common.mustNotCall());
+
+    req.on('close', common.mustCall(() => {
+      res.end('hello');
+    }));
+  });
+
+  server.listen(0, () => {
+    const req = http.request({
+      port: server.address().port
+    });
+
+    req.write('asd');
+    req.on('response', (res) => {
+      const buf = [];
+      res.on('data', (data) => buf.push(data));
+      res.on('end', common.mustCall(() => {
+        assert.deepStrictEqual(
+          Buffer.concat(buf),
+          Buffer.from('hello')
+        );
+        server.close();
+      }));
+    });
+  });
+}