diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8db5b756640b..102e9f3337b0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@
 ### Fixes
 
 - `[babel-plugin-jest-hoist]` Ignore `TSTypeQuery` when checking for hoisted references ([#13367](https://github.com/facebook/jest/pull/13367))
+- `[jest-core]` Fix `detectOpenHandles` false positives for some special objects such as `TLSWRAP`. ([#13414](https://github.com/facebook/jest/pull/13414))
 - `[jest-mock]` Fix mocking of getters and setters on classes ([#13398](https://github.com/facebook/jest/pull/13398))
 - `[jest-reporters]` Revert: Transform file paths into hyperlinks ([#13399](https://github.com/facebook/jest/pull/13399))
 - `[@jest/types]` Infer type of `each` table correctly when the table is a tuple or array ([#13381](https://github.com/facebook/jest/pull/13381))
diff --git a/packages/jest-core/src/__tests__/collectHandles.test.js b/packages/jest-core/src/__tests__/collectHandles.test.js
index 229ccb9a2c7a..db56aeff2184 100644
--- a/packages/jest-core/src/__tests__/collectHandles.test.js
+++ b/packages/jest-core/src/__tests__/collectHandles.test.js
@@ -10,6 +10,7 @@ import * as crypto from 'crypto';
 import {promises as dns} from 'dns';
 import http from 'http';
 import {PerformanceObserver} from 'perf_hooks';
+import {TLSSocket} from 'tls';
 import zlib from 'zlib';
 import collectHandles from '../collectHandles';
 
@@ -134,4 +135,15 @@ describe('collectHandles', () => {
       expect.objectContaining({message: 'TCPSERVERWRAP'}),
     );
   });
+
+  it('should not be false positives for some special objects such as `TLSWRAP`', async () => {
+    const handleCollector = collectHandles();
+
+    const socket = new TLSSocket();
+    socket.destroy();
+
+    const openHandles = await handleCollector();
+
+    expect(openHandles).toHaveLength(0);
+  });
 });
diff --git a/packages/jest-core/src/collectHandles.ts b/packages/jest-core/src/collectHandles.ts
index 5e69fd920e71..f5e79eafed9e 100644
--- a/packages/jest-core/src/collectHandles.ts
+++ b/packages/jest-core/src/collectHandles.ts
@@ -9,6 +9,8 @@
 
 import * as asyncHooks from 'async_hooks';
 import {promisify} from 'util';
+import * as v8 from 'v8';
+import * as vm from 'vm';
 import stripAnsi = require('strip-ansi');
 import type {Config} from '@jest/types';
 import {formatExecError} from 'jest-message-util';
@@ -45,6 +47,22 @@ const hasWeakRef = typeof WeakRef === 'function';
 
 const asyncSleep = promisify(setTimeout);
 
+let gcFunc: (() => void) | undefined = (globalThis as any).gc;
+function runGC() {
+  if (!gcFunc) {
+    v8.setFlagsFromString('--expose-gc');
+    gcFunc = vm.runInNewContext('gc');
+    v8.setFlagsFromString('--no-expose-gc');
+    if (!gcFunc) {
+      throw new Error(
+        'Cannot find `global.gc` function. Please run node with `--expose-gc` and report this issue in jest repo.',
+      );
+    }
+  }
+
+  gcFunc();
+}
+
 // Inspired by https://github.com/mafintosh/why-is-node-running/blob/master/index.js
 // Extracted as we want to format the result ourselves
 export default function collectHandles(): HandleCollectionResult {
@@ -125,6 +143,14 @@ export default function collectHandles(): HandleCollectionResult {
     // callback, we will not yet have seen the resource be destroyed here.
     await asyncSleep(100);
 
+    if (activeHandles.size > 0) {
+      // For some special objects such as `TLSWRAP`.
+      // Ref: https://github.com/facebook/jest/issues/11665
+      runGC();
+
+      await asyncSleep(0);
+    }
+
     hook.disable();
 
     // Get errors for every async resource still referenced at this moment