diff --git a/tokio/src/runtime/blocking/schedule.rs b/tokio/src/runtime/blocking/schedule.rs
index dae09791ee4..cece938fb0c 100644
--- a/tokio/src/runtime/blocking/schedule.rs
+++ b/tokio/src/runtime/blocking/schedule.rs
@@ -1,5 +1,6 @@
 use crate::runtime::task::{self, Task};
-use crate::time::Clock;
+#[cfg(feature = "test-util")]
+use crate::runtime::{scheduler, Handle};
 
 /// `task::Schedule` implementation that does nothing (except some bookkeeping
 /// in test-util builds). This is unique to the blocking scheduler as tasks
@@ -9,14 +10,20 @@ use crate::time::Clock;
 /// in `release`.
 pub(crate) struct BlockingSchedule {
     #[cfg(feature = "test-util")]
-    clock: Clock,
+    handle: Handle,
 }
 
 impl BlockingSchedule {
     pub(crate) fn new() -> Self {
         BlockingSchedule {
             #[cfg(feature = "test-util")]
-            clock: crate::time::inhibit_auto_advance(),
+            handle: {
+                let handle = Handle::current();
+                if let scheduler::Handle::CurrentThread(handle) = &handle.inner {
+                    handle.driver.clock.inhibit_auto_advance();
+                }
+                handle
+            },
         }
     }
 }
@@ -25,7 +32,10 @@ impl task::Schedule for BlockingSchedule {
     fn release(&self, _task: &Task<Self>) -> Option<Task<Self>> {
         #[cfg(feature = "test-util")]
         {
-            self.clock.allow_auto_advance();
+            if let scheduler::Handle::CurrentThread(handle) = &self.handle.inner {
+                handle.driver.clock.allow_auto_advance();
+                handle.driver.unpark();
+            }
         }
         None
     }
diff --git a/tokio/src/time/clock.rs b/tokio/src/time/clock.rs
index 9e55c82e89e..cd11a67527f 100644
--- a/tokio/src/time/clock.rs
+++ b/tokio/src/time/clock.rs
@@ -132,13 +132,6 @@ cfg_test_util! {
         inner.unfrozen = Some(std::time::Instant::now());
     }
 
-    /// Temporarily stop auto-advancing the clock (see `tokio::time::pause`).
-    pub(crate) fn inhibit_auto_advance() -> Clock {
-        let clock = clock().expect("can't inhibit auto-advance from outside the Tokio runtime");
-        clock.inhibit_auto_advance();
-        clock
-    }
-
     /// Advances time.
     ///
     /// Increments the saved `Instant::now()` value by `duration`. Subsequent
@@ -223,7 +216,8 @@ cfg_test_util! {
             inner.unfrozen = None;
         }
 
-        fn inhibit_auto_advance(&self) {
+        /// Temporarily stop auto-advancing the clock (see `tokio::time::pause`).
+        pub(crate) fn inhibit_auto_advance(&self) {
             let mut inner = self.inner.lock();
             inner.auto_advance_inhibit_count += 1;
         }
diff --git a/tokio/src/time/mod.rs b/tokio/src/time/mod.rs
index 42715de90f6..a1f27b839e9 100644
--- a/tokio/src/time/mod.rs
+++ b/tokio/src/time/mod.rs
@@ -87,8 +87,6 @@
 mod clock;
 pub(crate) use self::clock::Clock;
 #[cfg(feature = "test-util")]
-pub(crate) use clock::inhibit_auto_advance;
-#[cfg(feature = "test-util")]
 pub use clock::{advance, pause, resume};
 
 pub mod error;
diff --git a/tokio/tests/task_blocking.rs b/tokio/tests/task_blocking.rs
index 5859368b4cd..b50bf393afc 100644
--- a/tokio/tests/task_blocking.rs
+++ b/tokio/tests/task_blocking.rs
@@ -269,6 +269,25 @@ async fn blocking_task_wakes_paused_runtime() {
     );
 }
 
+#[cfg(feature = "test-util")]
+#[tokio::test(start_paused = true)]
+async fn unawaited_blocking_task_wakes_paused_runtime() {
+    let t0 = std::time::Instant::now();
+
+    // When this task finishes, time should auto-advance, even though the
+    // JoinHandle has not been awaited yet.
+    let a = task::spawn_blocking(|| {
+        thread::sleep(Duration::from_millis(20));
+    });
+
+    crate::time::sleep(Duration::from_secs(15)).await;
+    a.await.expect("blocking task should finish");
+    assert!(
+        t0.elapsed() < Duration::from_secs(10),
+        "completing a spawn_blocking should wake the scheduler if it's parked while time is paused"
+    );
+}
+
 #[cfg(feature = "test-util")]
 #[tokio::test(start_paused = true)]
 async fn panicking_blocking_task_wakes_paused_runtime() {