diff --git a/lib/api/api-request.js b/lib/api/api-request.js
index ced5590d210..be17d628774 100644
--- a/lib/api/api-request.js
+++ b/lib/api/api-request.js
@@ -73,7 +73,7 @@ class RequestHandler extends AsyncResource {
         this.removeAbortListener = util.addAbortListener(this.signal, () => {
           this.reason = this.signal.reason ?? new RequestAbortedError()
           if (this.res) {
-            util.destroy(this.res, this.reason)
+            util.destroy(this.res.on('error', util.nop), this.reason)
           } else if (this.abort) {
             this.abort(this.reason)
           }
diff --git a/test/client-request.js b/test/client-request.js
index c67cecdb7f3..c5e90e840ee 100644
--- a/test/client-request.js
+++ b/test/client-request.js
@@ -1252,3 +1252,39 @@ test('request post body DataView', async (t) => {
 
   await t.completed
 })
+
+test('#3736 - Aborted Response (without consuming body)', async (t) => {
+  const plan = tspl(t, { plan: 1 })
+
+  const controller = new AbortController()
+  const server = createServer((req, res) => {
+    setTimeout(() => {
+      res.writeHead(200, 'ok', {
+        'content-type': 'text/plain'
+      })
+      res.write('hello from server')
+      res.end()
+    }, 100)
+  })
+
+  server.listen(0)
+
+  await EE.once(server, 'listening')
+  const client = new Client(`http://localhost:${server.address().port}`)
+
+  after(server.close.bind(server))
+  after(client.destroy.bind(client))
+
+  const { signal } = controller
+  const promise = client.request({
+    path: '/',
+    method: 'GET',
+    signal
+  })
+
+  controller.abort()
+
+  await plan.rejects(promise, { message: 'This operation was aborted' })
+
+  await plan.completed
+})
diff --git a/test/http2.js b/test/http2.js
index d6840a1bd15..3f7ab3deb24 100644
--- a/test/http2.js
+++ b/test/http2.js
@@ -334,23 +334,15 @@ test(
 
     after(() => server.close())
     after(() => client.close())
-    t = tspl(t, { plan: 2 })
+    t = tspl(t, { plan: 1 })
 
-    try {
-      await client.request({
-        path: '/',
-        method: 'GET',
-        headers: {
-          'x-my-header': 'foo'
-        }
-      })
-    } catch (error) {
-      t.strictEqual(
-        error.message,
-        'Client network socket disconnected before secure TLS connection was established'
-      )
-      t.strictEqual(error.code, 'ECONNRESET')
-    }
+    await t.rejects(client.request({
+      path: '/',
+      method: 'GET',
+      headers: {
+        'x-my-header': 'foo'
+      }
+    }))
   }
 )