diff --git a/tokio/src/runtime/blocking/pool.rs b/tokio/src/runtime/blocking/pool.rs
index d681ed28458..1f209b6b794 100644
--- a/tokio/src/runtime/blocking/pool.rs
+++ b/tokio/src/runtime/blocking/pool.rs
@@ -317,6 +317,8 @@ impl Spawner {
         R: Send + 'static,
     {
         let fut = BlockingTask::new(func);
+        #[cfg(feature = "test-util")]
+        let fut = crate::time::inhibit_auto_advance(fut);
         let id = task::Id::next();
         #[cfg(all(tokio_unstable, feature = "tracing"))]
         let fut = {
@@ -337,9 +339,6 @@ impl Spawner {
         #[cfg(not(all(tokio_unstable, feature = "tracing")))]
         let _ = name;
 
-        #[cfg(feature = "test-util")]
-        let fut = crate::time::inhibit_auto_advance(fut);
-
         let (task, handle) = task::unowned(fut, NoopSchedule, id);
 
         let spawned = self.spawn_task(Task::new(task, is_mandatory), rt);
diff --git a/tokio/src/time/clock.rs b/tokio/src/time/clock.rs
index 55e6b3eea9d..f321fd6f4f9 100644
--- a/tokio/src/time/clock.rs
+++ b/tokio/src/time/clock.rs
@@ -141,7 +141,10 @@ cfg_test_util! {
     /// it returns `Ready` or is dropped.
     ///
     /// This is a no-op when called from outside the Tokio runtime.
-    pub(crate) fn inhibit_auto_advance<F: Future>(fut: F) -> impl Future<Output = F::Output> {
+    pub(crate) fn inhibit_auto_advance<F>(fut: F) -> impl Future<Output = F::Output> + Send + 'static
+    where
+        F: Future + Send + 'static,
+    {
         // Bump the inhibit count immediately, not inside the async block, to
         // avoid a race condition when used by spawn_blocking.
         let guard = clock().map(|clock| {