diff --git a/packages/playwright-core/src/client/browserType.ts b/packages/playwright-core/src/client/browserType.ts
index 9df049a641..06672cc64e 100644
--- a/packages/playwright-core/src/client/browserType.ts
+++ b/packages/playwright-core/src/client/browserType.ts
@@ -151,8 +151,14 @@ export class BrowserType extends ChannelOwner<channels.BrowserTypeChannel> imple
             page._onClose();
           context._onClose();
         }
-        browser?._didClose();
         connection.close(reason || closeError);
+        // Give a chance to any API call promises to reject upon page/context closure.
+        // This happens naturally when we receive page.onClose and browser.onClose from the server
+        // in separate tasks. However, upon pipe closure we used to dispatch them all synchronously
+        // here and promises did not have a chance to reject.
+        // The order of rejects vs closure is a part of the API contract and our test runner
+        // relies on it to attribute rejections to the right test.
+        setTimeout(() => browser?._didClose(), 0);
       };
       pipe.on('closed', params => onPipeClosed(params.reason));
       connection.onmessage = message => this._wrapApiCall(() => pipe.send({ message }).catch(() => onPipeClosed()), /* isInternal */ true);
diff --git a/tests/library/browsertype-connect.spec.ts b/tests/library/browsertype-connect.spec.ts
index a78814d326..4a3cdb1efa 100644
--- a/tests/library/browsertype-connect.spec.ts
+++ b/tests/library/browsertype-connect.spec.ts
@@ -408,6 +408,29 @@ for (const kind of ['launchServer', 'run-server'] as const) {
       }
     });
 
+    test('should reject waitForEvent before browser.close finishes', async ({ connect, startRemoteServer, server }) => {
+      const remoteServer = await startRemoteServer(kind);
+      const browser = await connect(remoteServer.wsEndpoint());
+      const newPage = await browser.newPage();
+      let rejected = false;
+      const promise = newPage.waitForEvent('download').catch(() => rejected = true);
+      await browser.close();
+      expect(rejected).toBe(true);
+      await promise;
+    });
+
+    test('should reject waitForEvent before browser.onDisconnect fires', async ({ connect, startRemoteServer, server }) => {
+      const remoteServer = await startRemoteServer(kind);
+      const browser = await connect(remoteServer.wsEndpoint());
+      const newPage = await browser.newPage();
+      const log: string[] = [];
+      const promise = newPage.waitForEvent('download').catch(() => log.push('rejected'));
+      browser.on('disconnected', () => log.push('disconnected'));
+      await remoteServer.close();
+      await promise;
+      await expect.poll(() => log).toEqual(['rejected', 'disconnected']);
+    });
+
     test('should respect selectors', async ({ playwright, connect, startRemoteServer }) => {
       const remoteServer = await startRemoteServer(kind);