diff --git a/tokio/src/time/clock.rs b/tokio/src/time/clock.rs
index 8957800cb..c5ef86be4 100644
--- a/tokio/src/time/clock.rs
+++ b/tokio/src/time/clock.rs
@@ -120,22 +120,11 @@ cfg_test_util! {
     /// Panics if time is not frozen or if called from outside of the Tokio
     /// runtime.
     pub async fn advance(duration: Duration) {
-        use crate::future::poll_fn;
-        use std::task::Poll;
-
         let clock = clock().expect("time cannot be frozen from outside the Tokio runtime");
+        let until = clock.now() + duration;
         clock.advance(duration);
 
-        let mut yielded = false;
-        poll_fn(|cx| {
-            if yielded {
-                Poll::Ready(())
-            } else {
-                yielded = true;
-                cx.waker().wake_by_ref();
-                Poll::Pending
-            }
-        }).await;
+        crate::time::sleep_until(until).await;
     }
 
     /// Return the current instant, factoring in frozen time.
diff --git a/tokio/tests/time_pause.rs b/tokio/tests/time_pause.rs
index bc84ac578..835db12f0 100644
--- a/tokio/tests/time_pause.rs
+++ b/tokio/tests/time_pause.rs
@@ -3,8 +3,29 @@
 
 use rand::SeedableRng;
 use rand::{rngs::StdRng, Rng};
-use tokio::time::{self, Duration, Instant};
-use tokio_test::assert_err;
+use tokio::time::{self, Duration, Instant, Sleep};
+use tokio_test::{assert_err, assert_pending, assert_ready_eq, task};
+
+use std::{
+    future::Future,
+    pin::Pin,
+    task::{Context, Poll},
+};
+
+macro_rules! assert_elapsed {
+    ($now:expr, $ms:expr) => {{
+        let elapsed = $now.elapsed();
+        let lower = ms($ms);
+
+        // Handles ms rounding
+        assert!(
+            elapsed >= lower && elapsed <= lower + ms(1),
+            "actual = {:?}, expected = {:?}",
+            elapsed,
+            lower
+        );
+    }};
+}
 
 #[tokio::test]
 async fn pause_time_in_main() {
@@ -57,3 +78,162 @@ async fn paused_time_stress_run() -> Vec<Duration> {
 
     times
 }
+
+#[tokio::test(start_paused = true)]
+async fn advance_after_poll() {
+    time::sleep(ms(1)).await;
+
+    let start = Instant::now();
+
+    let mut sleep = task::spawn(time::sleep_until(start + ms(300)));
+
+    assert_pending!(sleep.poll());
+
+    let before = Instant::now();
+    time::advance(ms(100)).await;
+    assert_elapsed!(before, 100);
+
+    assert_pending!(sleep.poll());
+}
+
+#[tokio::test(start_paused = true)]
+async fn sleep_no_poll() {
+    let start = Instant::now();
+
+    // TODO: Skip this
+    time::advance(ms(1)).await;
+
+    let mut sleep = task::spawn(time::sleep_until(start + ms(300)));
+
+    let before = Instant::now();
+    time::advance(ms(100)).await;
+    assert_elapsed!(before, 100);
+
+    assert_pending!(sleep.poll());
+}
+
+enum State {
+    Begin,
+    AwaitingAdvance(Pin<Box<dyn Future<Output = ()>>>),
+    AfterAdvance,
+}
+
+struct Tester {
+    sleep: Pin<Box<Sleep>>,
+    state: State,
+    before: Option<Instant>,
+    poll: bool,
+}
+
+impl Future for Tester {
+    type Output = ();
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        match &mut self.state {
+            State::Begin => {
+                if self.poll {
+                    assert_pending!(self.sleep.as_mut().poll(cx));
+                }
+                self.before = Some(Instant::now());
+                let advance_fut = Box::pin(time::advance(ms(100)));
+                self.state = State::AwaitingAdvance(advance_fut);
+                self.poll(cx)
+            }
+            State::AwaitingAdvance(ref mut advance_fut) => match advance_fut.as_mut().poll(cx) {
+                Poll::Pending => Poll::Pending,
+                Poll::Ready(()) => {
+                    self.state = State::AfterAdvance;
+                    self.poll(cx)
+                }
+            },
+            State::AfterAdvance => {
+                assert_elapsed!(self.before.unwrap(), 100);
+
+                assert_pending!(self.sleep.as_mut().poll(cx));
+
+                Poll::Ready(())
+            }
+        }
+    }
+}
+
+#[tokio::test(start_paused = true)]
+async fn sleep_same_task() {
+    let start = Instant::now();
+
+    // TODO: Skip this
+    time::advance(ms(1)).await;
+
+    let sleep = Box::pin(time::sleep_until(start + ms(300)));
+
+    Tester {
+        sleep,
+        state: State::Begin,
+        before: None,
+        poll: true,
+    }
+    .await;
+}
+
+#[tokio::test(start_paused = true)]
+async fn sleep_same_task_no_poll() {
+    let start = Instant::now();
+
+    // TODO: Skip this
+    time::advance(ms(1)).await;
+
+    let sleep = Box::pin(time::sleep_until(start + ms(300)));
+
+    Tester {
+        sleep,
+        state: State::Begin,
+        before: None,
+        poll: false,
+    }
+    .await;
+}
+
+#[tokio::test(start_paused = true)]
+async fn interval() {
+    let start = Instant::now();
+
+    // TODO: Skip this
+    time::advance(ms(1)).await;
+
+    let mut i = task::spawn(time::interval_at(start, ms(300)));
+
+    assert_ready_eq!(poll_next(&mut i), start);
+    assert_pending!(poll_next(&mut i));
+
+    let before = Instant::now();
+    time::advance(ms(100)).await;
+    assert_elapsed!(before, 100);
+    assert_pending!(poll_next(&mut i));
+
+    let before = Instant::now();
+    time::advance(ms(200)).await;
+    assert_elapsed!(before, 200);
+    assert_ready_eq!(poll_next(&mut i), start + ms(300));
+    assert_pending!(poll_next(&mut i));
+
+    let before = Instant::now();
+    time::advance(ms(400)).await;
+    assert_elapsed!(before, 400);
+    assert_ready_eq!(poll_next(&mut i), start + ms(600));
+    assert_pending!(poll_next(&mut i));
+
+    let before = Instant::now();
+    time::advance(ms(500)).await;
+    assert_elapsed!(before, 500);
+    assert_ready_eq!(poll_next(&mut i), start + ms(900));
+    assert_ready_eq!(poll_next(&mut i), start + ms(1200));
+    assert_pending!(poll_next(&mut i));
+}
+
+fn poll_next(interval: &mut task::Spawn<time::Interval>) -> Poll<Instant> {
+    interval.enter(|cx, mut interval| interval.poll_tick(cx))
+}
+
+fn ms(n: u64) -> Duration {
+    Duration::from_millis(n)
+}