diff --git a/html/webappapis/dynamic-markup-insertion/opening-the-input-stream/tasks.window.js b/html/webappapis/dynamic-markup-insertion/opening-the-input-stream/tasks.window.js
index 17f7330849bb38..5c1b567f50b786 100644
--- a/html/webappapis/dynamic-markup-insertion/opening-the-input-stream/tasks.window.js
+++ b/html/webappapis/dynamic-markup-insertion/opening-the-input-stream/tasks.window.js
@@ -10,6 +10,10 @@
 // second actually calls document.open() to test if the method call removes
 // that specific task from the queue.
 
+setup({
+  allow_uncaught_exception: true
+});
+
 function taskTest(description, testBody) {
   async_test(t => {
     const frame = document.body.appendChild(document.createElement("iframe"));
@@ -86,16 +90,20 @@ taskTest("MessagePort", (t, frame, open) => {
 });
 
 taskTest("Promise rejection", (t, frame, open) => {
-  // The frame.contentWindow.setTimeout is necessary to make the test work on
-  // Safari. See: https://bugs.webkit.org/show_bug.cgi?id=187822
-  frame.contentWindow.setTimeout(() => {
-    const promise = frame.contentWindow.eval("Promise.reject(42);");
-    open(frame.contentDocument);
-    frame.contentWindow.onunhandledrejection = t.step_func_done(ev => {
-      assert_equals(ev.promise, promise);
-      assert_equals(ev.reason, 42);
-    });
+  // There is currently some ambiguity on which Window object the
+  // unhandledrejection event should be fired on. Here, let's account for that
+  // ambiguity and allow event fired on _any_ global to pass this test.
+  // See:
+  // - https://github.com/whatwg/html/issues/958,
+  // - https://bugs.webkit.org/show_bug.cgi?id=187822
+  const promise = frame.contentWindow.eval("Promise.reject(42);");
+  open(frame.contentDocument);
+  const listener = t.step_func_done(ev => {
+    assert_equals(ev.promise, promise);
+    assert_equals(ev.reason, 42);
   });
+  frame.contentWindow.onunhandledrejection = listener;
+  window.onunhandledrejection = listener;
 });
 
 taskTest("marquee start", (t, frame, open) => {