diff --git a/distributed/tests/test_client.py b/distributed/tests/test_client.py
index 3121dcb6bdd..14ea3c7f886 100644
--- a/distributed/tests/test_client.py
+++ b/distributed/tests/test_client.py
@@ -89,6 +89,7 @@
     _UnhashableCallable,
     async_wait_for,
     asyncinc,
+    block_on_event,
     captured_logger,
     cluster,
     dec,
@@ -727,8 +728,9 @@ async def test_wait(c, s, a, b):
 
 @gen_cluster(client=True)
 async def test_wait_first_completed(c, s, a, b):
-    x = c.submit(slowinc, 1)
-    y = c.submit(slowinc, 1)
+    event = Event()
+    x = c.submit(block_on_event, event)
+    y = c.submit(block_on_event, event)
     z = c.submit(inc, 2)
 
     done, not_done = await wait([x, y, z], return_when="FIRST_COMPLETED")
@@ -738,6 +740,7 @@ async def test_wait_first_completed(c, s, a, b):
     assert z.status == "finished"
     assert x.status == "pending"
     assert y.status == "pending"
+    await event.set()
 
 
 @gen_cluster(client=True)
diff --git a/distributed/utils_test.py b/distributed/utils_test.py
index e851bb0a9b8..031b0e4acc1 100644
--- a/distributed/utils_test.py
+++ b/distributed/utils_test.py
@@ -38,7 +38,7 @@
 
 import dask
 
-from distributed import Scheduler, system
+from distributed import Event, Scheduler, system
 from distributed import versions as version_module
 from distributed.batched import BatchedSend
 from distributed.client import Client, _global_clients, default_client
@@ -289,6 +289,10 @@ def lock_inc(x, lock):
         return x + 1
 
 
+def block_on_event(event: Event) -> None:
+    event.wait()
+
+
 class _UnhashableCallable:
     # FIXME https://github.com/python/mypy/issues/4266
     __hash__ = None  # type: ignore