diff --git a/packages/puppeteer-core/src/api/Page.ts b/packages/puppeteer-core/src/api/Page.ts
index 217af5039fc..2c9c872eac0 100644
--- a/packages/puppeteer-core/src/api/Page.ts
+++ b/packages/puppeteer-core/src/api/Page.ts
@@ -1673,7 +1673,7 @@ export class Page extends EventEmitter {
           return false;
         },
         timeout,
-        abortDeferred.valueOrThrow()
+        abortDeferred
       );
     };
 
@@ -1685,7 +1685,11 @@ export class Page extends EventEmitter {
 
     evaluate();
 
-    await Deferred.race([idleDeferred, ...eventPromises, closedDeferred]).then(
+    // We don't want to reject the closed deferred when
+    // the race if finished so we pass the Promise instead
+    const closedPromise = closedDeferred.valueOrThrow();
+
+    await Deferred.race([idleDeferred, ...eventPromises, closedPromise]).then(
       r => {
         cleanup();
         return r;
diff --git a/packages/puppeteer-core/src/common/util.ts b/packages/puppeteer-core/src/common/util.ts
index a1077a58e6b..5ac0083ae3d 100644
--- a/packages/puppeteer-core/src/common/util.ts
+++ b/packages/puppeteer-core/src/common/util.ts
@@ -383,7 +383,7 @@ export async function waitForEvent<T>(
   eventName: string | symbol,
   predicate: (event: T) => Promise<boolean> | boolean,
   timeout: number,
-  abortPromise: Promise<Error>
+  abortPromise: Promise<Error> | Deferred<Error>
 ): Promise<T> {
   const deferred = Deferred.create<T>({
     message: `Timeout exceeded while waiting for event ${String(eventName)}`,
diff --git a/packages/puppeteer-core/src/util/Deferred.ts b/packages/puppeteer-core/src/util/Deferred.ts
index 424b7433775..7ddbc000df7 100644
--- a/packages/puppeteer-core/src/util/Deferred.ts
+++ b/packages/puppeteer-core/src/util/Deferred.ts
@@ -89,7 +89,9 @@ export class Deferred<T> {
     try {
       const promises = awaitables.map(value => {
         if (value instanceof Deferred) {
-          deferredWithTimeout.add(value);
+          if (value.#timeoutId) {
+            deferredWithTimeout.add(value);
+          }
 
           return value.valueOrThrow();
         }