diff --git a/CHANGELOG.md b/CHANGELOG.md
index 828a9175cba3..990180184b1a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,7 @@
 - `[@jest/types]` Mark deprecated configuration options as `@deprecated` ([#11913](https://github.com/facebook/jest/pull/11913))
 - `[jest-cli]` Improve `--help` printout by removing defunct `--browser` option ([#11914](https://github.com/facebook/jest/pull/11914))
 - `[jest-haste-map]` Use distinct cache paths for different values of `computeDependencies` ([#11916](https://github.com/facebook/jest/pull/11916))
+- `[jest-util]` Install fix for `instanceof` as part of other globals into test environments ([#5995](https://github.com/facebook/jest/pull/5995))
 
 ### Chore & Maintenance
 
diff --git a/e2e/__tests__/instanceof.test.ts b/e2e/__tests__/instanceof.test.ts
new file mode 100644
index 000000000000..3f191b00bf82
--- /dev/null
+++ b/e2e/__tests__/instanceof.test.ts
@@ -0,0 +1,14 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+import runJest from '../runJest';
+
+test('suite with `instanceof` checks', () => {
+  const {exitCode} = runJest('instanceof');
+
+  expect(exitCode).toBe(0);
+});
diff --git a/e2e/instanceof/__tests__/test.js b/e2e/instanceof/__tests__/test.js
new file mode 100644
index 000000000000..fbc6d976e596
--- /dev/null
+++ b/e2e/instanceof/__tests__/test.js
@@ -0,0 +1,132 @@
+/**
+ * Copyright (c) 2014-present, Facebook, Inc. All rights reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+'use strict';
+
+const fs = require('fs');
+const http = require('http');
+const util = require('util');
+const v8 = require('v8');
+
+const readFile = util.promisify(fs.readFile);
+
+function getSuperClass(cls) {
+  const prototype = Object.getPrototypeOf(cls.prototype);
+  return prototype ? prototype.constructor : null;
+}
+
+const buffers = fs.readdirSync(__dirname);
+const buffer = fs.readFileSync(__filename);
+const error = (() => {
+  try {
+    fs.readFileSync('/');
+  } catch (e) {
+    return e;
+  }
+})();
+const promise = readFile(__filename);
+
+const nodeArrayType = buffers.constructor;
+const nodeErrorType = error.constructor;
+const nodePromiseType = promise.constructor;
+const nodeUint8ArrayType = getSuperClass(buffer.constructor);
+const nodeTypedArrayType = getSuperClass(nodeUint8ArrayType);
+const nodeObjectType = getSuperClass(nodeTypedArrayType);
+
+const globalTypedArrayType = getSuperClass(Uint8Array);
+
+test('fs Error', () => {
+  expect.hasAssertions();
+
+  try {
+    fs.readFileSync('does not exist');
+  } catch (err) {
+    expect(err).toBeInstanceOf(Error);
+  }
+});
+
+test('http error', done => {
+  const request = http.request('http://does-not-exist/blah', res => {
+    console.log(`STATUS: ${res.statusCode}`);
+    res.on('end', () => {
+      done(new Error('Ended before failure'));
+    });
+  });
+
+  request.once('error', err => {
+    expect(err).toBeInstanceOf(Error);
+    done();
+  });
+});
+
+test('Array', () => {
+  expect([]).toBeInstanceOf(Array);
+});
+
+test('array type', () => {
+  expect(buffers).toBeInstanceOf(Array);
+  expect(buffers).toBeInstanceOf(Object);
+  expect([]).toBeInstanceOf(nodeArrayType);
+  expect([]).toBeInstanceOf(nodeObjectType);
+});
+
+test('error type', () => {
+  expect(error).toBeInstanceOf(Error);
+  expect(error).toBeInstanceOf(Object);
+  expect(new Error()).toBeInstanceOf(nodeErrorType);
+  expect(new Error()).toBeInstanceOf(nodeObjectType);
+});
+
+test('promise type', () => {
+  expect(promise).toBeInstanceOf(Promise);
+  expect(promise).toBeInstanceOf(Object);
+  expect(new Promise(resolve => resolve())).toBeInstanceOf(nodePromiseType);
+  expect(new Promise(resolve => resolve())).toBeInstanceOf(nodeObjectType);
+});
+
+test('Uint8Array type', () => {
+  expect(buffer).toBeInstanceOf(Buffer);
+  expect(buffer).toBeInstanceOf(Uint8Array);
+  expect(buffer).toBeInstanceOf(globalTypedArrayType);
+  expect(buffer).toBeInstanceOf(Object);
+  expect(new Uint8Array([])).toBeInstanceOf(nodeUint8ArrayType);
+  expect(new Uint8Array([])).toBeInstanceOf(nodeTypedArrayType);
+  expect(new Uint8Array([])).toBeInstanceOf(nodeObjectType);
+});
+
+test('recognizes typed arrays as objects', () => {
+  expect(new Uint8Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new Uint8ClampedArray([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new Uint16Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new Uint32Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new BigUint64Array([])).toBeInstanceOf(Object);
+  expect(new Int8Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new Int16Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new Int32Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new BigInt64Array([])).toBeInstanceOf(Object);
+  expect(new Float32Array([1, 2, 3])).toBeInstanceOf(Object);
+  expect(new Float64Array([1, 2, 3])).toBeInstanceOf(Object);
+});
+
+test('recognizes typed arrays as instances of TypedArray', () => {
+  expect(new Uint8Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Uint8ClampedArray([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Uint16Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Uint32Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new BigUint64Array([])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Int8Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Int16Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Int32Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new BigInt64Array([])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Float32Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+  expect(new Float64Array([1, 2, 3])).toBeInstanceOf(globalTypedArrayType);
+});
+
+test('v8 serialize/deserialize', () => {
+  const m1 = new Map();
+  const m2 = v8.deserialize(v8.serialize(m1));
+  expect(m1).toEqual(m2);
+});
diff --git a/e2e/instanceof/package.json b/e2e/instanceof/package.json
new file mode 100644
index 000000000000..148788b25446
--- /dev/null
+++ b/e2e/instanceof/package.json
@@ -0,0 +1,5 @@
+{
+  "jest": {
+    "testEnvironment": "node"
+  }
+}
diff --git a/packages/jest-util/src/__tests__/addInstanceOfAlias.test.ts b/packages/jest-util/src/__tests__/addInstanceOfAlias.test.ts
new file mode 100644
index 000000000000..82b414c85158
--- /dev/null
+++ b/packages/jest-util/src/__tests__/addInstanceOfAlias.test.ts
@@ -0,0 +1,44 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+import addInstanceOfAlias from '../addInstanceOfAlias';
+
+describe('addInstanceOfAlias', () => {
+  let Color;
+  let Purple;
+  let OtherPurple;
+  let Black;
+  beforeEach(() => {
+    Color = class Color {};
+    Purple = class Purple extends Color {};
+    OtherPurple = class OtherPurple extends Color {};
+    Black = class Black extends Color {};
+  });
+
+  it('adds the given alias to the target as an object to include in an instanceof call', () => {
+    const purple = new Purple();
+    expect(purple instanceof OtherPurple).toBe(false);
+    addInstanceOfAlias(OtherPurple, Purple);
+    expect(purple instanceof OtherPurple).toBe(true);
+  });
+
+  it('preserves the prior instanceof lookup', () => {
+    const purple = new Purple();
+    addInstanceOfAlias(OtherPurple, Purple);
+    expect(purple instanceof Purple).toBe(true);
+    expect(purple instanceof Color).toBe(true);
+    expect(purple instanceof Black).toBe(false);
+  });
+
+  describe('when using the same value for the target and alias', () => {
+    it('throws an error', () => {
+      expect(() => {
+        addInstanceOfAlias(Purple, Purple);
+      }).toThrow(Error);
+    });
+  });
+});
diff --git a/packages/jest-util/src/addInstanceOfAlias.ts b/packages/jest-util/src/addInstanceOfAlias.ts
new file mode 100644
index 000000000000..fc833910fa9b
--- /dev/null
+++ b/packages/jest-util/src/addInstanceOfAlias.ts
@@ -0,0 +1,35 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+// using `Function` is on purpose - it's exactly what we want in this case
+// eslint-disable-next-line @typescript-eslint/ban-types
+type InstanceOfThing = Function;
+
+export default function addInstanceOfAlias(
+  target: InstanceOfThing,
+  alias: InstanceOfThing,
+): void {
+  if (target === alias) {
+    throw new Error(
+      'Attempted to call addInstanceOfAlias with the same object for both ' +
+        'the target and the alias. This will create an infinite loop in ' +
+        'instanceof checks.',
+    );
+  }
+
+  const originalHasInstance = target[Symbol.hasInstance];
+  Object.defineProperty(target, Symbol.hasInstance, {
+    configurable: true,
+    value: function aliasedHasInstance(potentialInstance: unknown) {
+      return (
+        potentialInstance instanceof alias ||
+        originalHasInstance.call(this, potentialInstance)
+      );
+    },
+    writable: true,
+  });
+}
diff --git a/packages/jest-util/src/installCommonGlobals.ts b/packages/jest-util/src/installCommonGlobals.ts
index 5931f672e3e8..944575d4a39b 100644
--- a/packages/jest-util/src/installCommonGlobals.ts
+++ b/packages/jest-util/src/installCommonGlobals.ts
@@ -7,6 +7,7 @@
 
 import * as fs from 'graceful-fs';
 import type {Config} from '@jest/types';
+import addInstanceOfAlias from './addInstanceOfAlias';
 import createProcessObject from './createProcessObject';
 import deepCyclicCopy from './deepCyclicCopy';
 
@@ -62,5 +63,10 @@ export default function (
     };
   });
 
+  addInstanceOfAlias(globalObject.Error, Error);
+  addInstanceOfAlias(globalObject.Promise, Promise);
+  addInstanceOfAlias(globalObject.Object, Object);
+  addInstanceOfAlias(globalObject.Function, Function);
+
   return Object.assign(globalObject, deepCyclicCopy(globals));
 }