diff --git a/source/core/index.ts b/source/core/index.ts
index d3b635c99..987770e6c 100644
--- a/source/core/index.ts
+++ b/source/core/index.ts
@@ -15,6 +15,7 @@ import http2wrapper = require('http2-wrapper');
 import lowercaseKeys = require('lowercase-keys');
 import ResponseLike = require('responselike');
 import is, {assert} from '@sindresorhus/is';
+import applyDestroyPatch from './utils/apply-destroy-patch';
 import getBodySize from './utils/get-body-size';
 import isFormData from './utils/is-form-data';
 import proxyEvents from './utils/proxy-events';
@@ -1379,6 +1380,9 @@ export default class Request extends Duplex implements RequestEvents<Request> {
 			highWaterMark: 0
 		});
 
+		// TODO: Remove this when targeting Node.js 14
+		applyDestroyPatch(this);
+
 		this[kDownloadedSize] = 0;
 		this[kUploadedSize] = 0;
 		this.requestInitialized = false;
diff --git a/source/core/utils/apply-destroy-patch.ts b/source/core/utils/apply-destroy-patch.ts
new file mode 100644
index 000000000..9b2713505
--- /dev/null
+++ b/source/core/utils/apply-destroy-patch.ts
@@ -0,0 +1,18 @@
+import {Readable, Writable} from 'stream';
+
+export default function applyDestroyPatch(stream: Readable | Writable): void {
+	const kDestroy = Symbol('destroy');
+
+	if (Number(process.versions.node.split('.')[0]) >= 14) {
+		return;
+	}
+
+	// @ts-expect-error
+	stream[kDestroy] = stream.destroy;
+	stream.destroy = (...args) => {
+		if (!stream.destroyed) {
+			// @ts-expect-error
+			return stream[kDestroy](...args);
+		}
+	};
+}
diff --git a/test/stream.ts b/test/stream.ts
index 686b052cc..214882e88 100644
--- a/test/stream.ts
+++ b/test/stream.ts
@@ -11,6 +11,7 @@ import * as FormData from 'form-data';
 import is from '@sindresorhus/is';
 import got, {RequestError} from '../source/index';
 import withServer from './helpers/with-server';
+import delay = require('delay');
 
 const pStreamPipeline = promisify(stream.pipeline);
 
@@ -419,6 +420,22 @@ test('async iterator works', withServer, async (t, server, got) => {
 	t.is(Buffer.concat(chunks).toString(), payload);
 });
 
+test('destroys only once', async t => {
+	const stream = got.stream('https://example.com');
+	stream.destroy();
+	stream.destroy(new Error('oh no'));
+
+	let errored = false;
+
+	stream.once('error', () => {
+		errored = true;
+	});
+
+	await delay(1);
+
+	t.false(errored);
+});
+
 if (Number.parseInt(process.versions.node.split('.')[0]!, 10) <= 12) {
 	test('does not emit end event on error', withServer, async (t, server, got) => {
 		server.get('/', infiniteHandler);