diff --git a/CHANGELOG.md b/CHANGELOG.md
index 758d2c412a16..b9c56f0c8285 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,7 @@
 
 - `[expect]` Tweak and improve types ([#11949](https://github.com/facebook/jest/pull/11949))
 - `[jest-runtime]` Ensure absolute paths can be resolved within test modules ([#11943](https://github.com/facebook/jest/pull/11943))
+- `[jest-runtime]` Fix `instanceof` for `ModernFakeTimers` and `LegacyFakeTimers` methods ([#11946](https://github.com/facebook/jest/pull/11946))
 
 ### Chore & Maintenance
 
diff --git a/docs/Puppeteer.md b/docs/Puppeteer.md
index 6c8e67e40d10..53c16767b74e 100644
--- a/docs/Puppeteer.md
+++ b/docs/Puppeteer.md
@@ -55,10 +55,9 @@ Here's an example of the GlobalSetup script
 
 ```js
 // setup.js
-const {writeFile} = require('fs').promises;
+const {mkdir, writeFile} = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const mkdirp = require('mkdirp');
 const puppeteer = require('puppeteer');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
@@ -70,7 +69,7 @@ module.exports = async function () {
   global.__BROWSER_GLOBAL__ = browser;
 
   // use the file system to expose the wsEndpoint for TestEnvironments
-  mkdirp.sync(DIR);
+  await mkdir(DIR, {recursive: true});
   await writeFile(path.join(DIR, 'wsEndpoint'), browser.wsEndpoint());
 };
 ```
@@ -122,9 +121,9 @@ Finally, we can close the puppeteer instance and clean-up the file
 
 ```js
 // teardown.js
+const fs = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const rimraf = require('rimraf');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
 module.exports = async function () {
@@ -132,7 +131,7 @@ module.exports = async function () {
   await global.__BROWSER_GLOBAL__.close();
 
   // clean-up the wsEndpoint file
-  rimraf.sync(DIR);
+  await fs.rm(DIR, {recursive: true, force: true});
 };
 ```
 
diff --git a/e2e/resolve-conditions/package.json b/e2e/resolve-conditions/package.json
index 987f46111b8a..33449adf2da3 100644
--- a/e2e/resolve-conditions/package.json
+++ b/e2e/resolve-conditions/package.json
@@ -13,6 +13,6 @@
     "transform": {}
   },
   "dependencies": {
-    "resolve.exports": "^1.0.2"
+    "resolve.exports": "^1.1.0"
   }
 }
diff --git a/e2e/resolve-conditions/resolver.js b/e2e/resolve-conditions/resolver.js
index 98c8aed1bf67..09cee4fb91a3 100644
--- a/e2e/resolve-conditions/resolver.js
+++ b/e2e/resolve-conditions/resolver.js
@@ -24,13 +24,7 @@ function createPathFilter(conditions) {
     const path = relativePath === 'index' ? '.' : relativePath;
 
     return (
-      resolveExports(pkg, path, {
-        // `resolve.exports adds `node` unless `browser` is `false`, so let's add this ugly thing
-        browser: conditions.includes('browser'),
-        conditions,
-        // `resolve.exports adds `import` unless `require` is `false`, so let's add this ugly thing
-        require: conditions.includes('require'),
-      }) || relativePath
+      resolveExports(pkg, path, {conditions, unsafe: true}) || relativePath
     );
   };
 }
diff --git a/e2e/resolve-conditions/yarn.lock b/e2e/resolve-conditions/yarn.lock
index b98bb300b2b9..df2f59b137b1 100644
--- a/e2e/resolve-conditions/yarn.lock
+++ b/e2e/resolve-conditions/yarn.lock
@@ -5,10 +5,10 @@ __metadata:
   version: 4
   cacheKey: 7
 
-"resolve.exports@npm:^1.0.2":
-  version: 1.0.2
-  resolution: "resolve.exports@npm:1.0.2"
-  checksum: 012a46e3ae41c53762abf5b50ea1b4adf2de617bbea1dbc7bf6e609c1ceaedee7782acbc92d443951d5dd0c3a8fb1090ce73285a9ccc24b530e33b5e09ae196f
+"resolve.exports@npm:^1.1.0":
+  version: 1.1.0
+  resolution: "resolve.exports@npm:1.1.0"
+  checksum: d04d2ce651fac14fe6ba13b377690f790cbbe91e6211b8fbec97ee08282e278875c74073a9b6243143a64e33d95eefb479e1dd4965664edc73b28b712100b36c
   languageName: node
   linkType: hard
 
@@ -16,6 +16,6 @@ __metadata:
   version: 0.0.0-use.local
   resolution: "root-workspace-0b6124@workspace:."
   dependencies:
-    resolve.exports: ^1.0.2
+    resolve.exports: ^1.1.0
   languageName: unknown
   linkType: soft
diff --git a/packages/jest-runtime/package.json b/packages/jest-runtime/package.json
index 881360f1050c..a498152b1a2e 100644
--- a/packages/jest-runtime/package.json
+++ b/packages/jest-runtime/package.json
@@ -16,7 +16,6 @@
   "dependencies": {
     "@jest/console": "^27.2.5",
     "@jest/environment": "^27.2.5",
-    "@jest/fake-timers": "^27.2.5",
     "@jest/globals": "^27.2.5",
     "@jest/source-map": "^27.0.6",
     "@jest/test-result": "^27.2.5",
@@ -43,6 +42,7 @@
     "yargs": "^16.2.0"
   },
   "devDependencies": {
+    "@jest/fake-timers": "^27.2.5",
     "@jest/test-utils": "^27.2.5",
     "@types/exit": "^0.1.30",
     "@types/glob": "^7.1.1",
diff --git a/packages/jest-runtime/src/index.ts b/packages/jest-runtime/src/index.ts
index c8cfa5c17246..8640b45ea405 100644
--- a/packages/jest-runtime/src/index.ts
+++ b/packages/jest-runtime/src/index.ts
@@ -30,7 +30,7 @@ import type {
   Module,
   ModuleWrapper,
 } from '@jest/environment';
-import {LegacyFakeTimers, ModernFakeTimers} from '@jest/fake-timers';
+import type {LegacyFakeTimers, ModernFakeTimers} from '@jest/fake-timers';
 import type * as JestGlobals from '@jest/globals';
 import type {SourceMapRegistry} from '@jest/source-map';
 import type {RuntimeTransformResult, V8CoverageResult} from '@jest/test-result';
@@ -1963,7 +1963,7 @@ export default class Runtime {
       getRealSystemTime: () => {
         const fakeTimers = _getFakeTimers();
 
-        if (fakeTimers instanceof ModernFakeTimers) {
+        if (fakeTimers === this._environment.fakeTimersModern) {
           return fakeTimers.getRealSystemTime();
         } else {
           throw new TypeError(
@@ -1984,7 +1984,7 @@ export default class Runtime {
       runAllImmediates: () => {
         const fakeTimers = _getFakeTimers();
 
-        if (fakeTimers instanceof LegacyFakeTimers) {
+        if (fakeTimers === this._environment.fakeTimers) {
           fakeTimers.runAllImmediates();
         } else {
           throw new TypeError(
@@ -2000,7 +2000,7 @@ export default class Runtime {
       setSystemTime: (now?: number | Date) => {
         const fakeTimers = _getFakeTimers();
 
-        if (fakeTimers instanceof ModernFakeTimers) {
+        if (fakeTimers === this._environment.fakeTimersModern) {
           fakeTimers.setSystemTime(now);
         } else {
           throw new TypeError(
diff --git a/website/versioned_docs/version-25.x/Puppeteer.md b/website/versioned_docs/version-25.x/Puppeteer.md
index 3349f73da2a7..c0b92dfd97dd 100644
--- a/website/versioned_docs/version-25.x/Puppeteer.md
+++ b/website/versioned_docs/version-25.x/Puppeteer.md
@@ -55,10 +55,9 @@ Here's an example of the GlobalSetup script
 
 ```js
 // setup.js
-const {writeFile} = require('fs').promises;
+const {mkdir, writeFile} = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const mkdirp = require('mkdirp');
 const puppeteer = require('puppeteer');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
@@ -70,7 +69,7 @@ module.exports = async function () {
   global.__BROWSER_GLOBAL__ = browser;
 
   // use the file system to expose the wsEndpoint for TestEnvironments
-  mkdirp.sync(DIR);
+  await mkdir(DIR, {recursive: true});
   await writeFile(path.join(DIR, 'wsEndpoint'), browser.wsEndpoint());
 };
 ```
@@ -122,9 +121,9 @@ Finally, we can close the puppeteer instance and clean-up the file
 
 ```js
 // teardown.js
+const fs = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const rimraf = require('rimraf');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
 module.exports = async function () {
@@ -132,7 +131,7 @@ module.exports = async function () {
   await global.__BROWSER_GLOBAL__.close();
 
   // clean-up the wsEndpoint file
-  rimraf.sync(DIR);
+  await fs.rm(DIR, {recursive: true, force: true});
 };
 ```
 
diff --git a/website/versioned_docs/version-26.x/Puppeteer.md b/website/versioned_docs/version-26.x/Puppeteer.md
index 3349f73da2a7..c0b92dfd97dd 100644
--- a/website/versioned_docs/version-26.x/Puppeteer.md
+++ b/website/versioned_docs/version-26.x/Puppeteer.md
@@ -55,10 +55,9 @@ Here's an example of the GlobalSetup script
 
 ```js
 // setup.js
-const {writeFile} = require('fs').promises;
+const {mkdir, writeFile} = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const mkdirp = require('mkdirp');
 const puppeteer = require('puppeteer');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
@@ -70,7 +69,7 @@ module.exports = async function () {
   global.__BROWSER_GLOBAL__ = browser;
 
   // use the file system to expose the wsEndpoint for TestEnvironments
-  mkdirp.sync(DIR);
+  await mkdir(DIR, {recursive: true});
   await writeFile(path.join(DIR, 'wsEndpoint'), browser.wsEndpoint());
 };
 ```
@@ -122,9 +121,9 @@ Finally, we can close the puppeteer instance and clean-up the file
 
 ```js
 // teardown.js
+const fs = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const rimraf = require('rimraf');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
 module.exports = async function () {
@@ -132,7 +131,7 @@ module.exports = async function () {
   await global.__BROWSER_GLOBAL__.close();
 
   // clean-up the wsEndpoint file
-  rimraf.sync(DIR);
+  await fs.rm(DIR, {recursive: true, force: true});
 };
 ```
 
diff --git a/website/versioned_docs/version-27.0/Puppeteer.md b/website/versioned_docs/version-27.0/Puppeteer.md
index 6c8e67e40d10..53c16767b74e 100644
--- a/website/versioned_docs/version-27.0/Puppeteer.md
+++ b/website/versioned_docs/version-27.0/Puppeteer.md
@@ -55,10 +55,9 @@ Here's an example of the GlobalSetup script
 
 ```js
 // setup.js
-const {writeFile} = require('fs').promises;
+const {mkdir, writeFile} = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const mkdirp = require('mkdirp');
 const puppeteer = require('puppeteer');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
@@ -70,7 +69,7 @@ module.exports = async function () {
   global.__BROWSER_GLOBAL__ = browser;
 
   // use the file system to expose the wsEndpoint for TestEnvironments
-  mkdirp.sync(DIR);
+  await mkdir(DIR, {recursive: true});
   await writeFile(path.join(DIR, 'wsEndpoint'), browser.wsEndpoint());
 };
 ```
@@ -122,9 +121,9 @@ Finally, we can close the puppeteer instance and clean-up the file
 
 ```js
 // teardown.js
+const fs = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const rimraf = require('rimraf');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
 module.exports = async function () {
@@ -132,7 +131,7 @@ module.exports = async function () {
   await global.__BROWSER_GLOBAL__.close();
 
   // clean-up the wsEndpoint file
-  rimraf.sync(DIR);
+  await fs.rm(DIR, {recursive: true, force: true});
 };
 ```
 
diff --git a/website/versioned_docs/version-27.1/Puppeteer.md b/website/versioned_docs/version-27.1/Puppeteer.md
index 6c8e67e40d10..53c16767b74e 100644
--- a/website/versioned_docs/version-27.1/Puppeteer.md
+++ b/website/versioned_docs/version-27.1/Puppeteer.md
@@ -55,10 +55,9 @@ Here's an example of the GlobalSetup script
 
 ```js
 // setup.js
-const {writeFile} = require('fs').promises;
+const {mkdir, writeFile} = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const mkdirp = require('mkdirp');
 const puppeteer = require('puppeteer');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
@@ -70,7 +69,7 @@ module.exports = async function () {
   global.__BROWSER_GLOBAL__ = browser;
 
   // use the file system to expose the wsEndpoint for TestEnvironments
-  mkdirp.sync(DIR);
+  await mkdir(DIR, {recursive: true});
   await writeFile(path.join(DIR, 'wsEndpoint'), browser.wsEndpoint());
 };
 ```
@@ -122,9 +121,9 @@ Finally, we can close the puppeteer instance and clean-up the file
 
 ```js
 // teardown.js
+const fs = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const rimraf = require('rimraf');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
 module.exports = async function () {
@@ -132,7 +131,7 @@ module.exports = async function () {
   await global.__BROWSER_GLOBAL__.close();
 
   // clean-up the wsEndpoint file
-  rimraf.sync(DIR);
+  await fs.rm(DIR, {recursive: true, force: true});
 };
 ```
 
diff --git a/website/versioned_docs/version-27.2/Puppeteer.md b/website/versioned_docs/version-27.2/Puppeteer.md
index 6c8e67e40d10..53c16767b74e 100644
--- a/website/versioned_docs/version-27.2/Puppeteer.md
+++ b/website/versioned_docs/version-27.2/Puppeteer.md
@@ -55,10 +55,9 @@ Here's an example of the GlobalSetup script
 
 ```js
 // setup.js
-const {writeFile} = require('fs').promises;
+const {mkdir, writeFile} = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const mkdirp = require('mkdirp');
 const puppeteer = require('puppeteer');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
@@ -70,7 +69,7 @@ module.exports = async function () {
   global.__BROWSER_GLOBAL__ = browser;
 
   // use the file system to expose the wsEndpoint for TestEnvironments
-  mkdirp.sync(DIR);
+  await mkdir(DIR, {recursive: true});
   await writeFile(path.join(DIR, 'wsEndpoint'), browser.wsEndpoint());
 };
 ```
@@ -122,9 +121,9 @@ Finally, we can close the puppeteer instance and clean-up the file
 
 ```js
 // teardown.js
+const fs = require('fs').promises;
 const os = require('os');
 const path = require('path');
-const rimraf = require('rimraf');
 
 const DIR = path.join(os.tmpdir(), 'jest_puppeteer_global_setup');
 module.exports = async function () {
@@ -132,7 +131,7 @@ module.exports = async function () {
   await global.__BROWSER_GLOBAL__.close();
 
   // clean-up the wsEndpoint file
-  rimraf.sync(DIR);
+  await fs.rm(DIR, {recursive: true, force: true});
 };
 ```