diff --git a/tokio/src/task/local.rs b/tokio/src/task/local.rs
index 11dfa274e..c619f1d47 100644
--- a/tokio/src/task/local.rs
+++ b/tokio/src/task/local.rs
@@ -280,10 +280,43 @@ pin_project! {
 
 tokio_thread_local!(static CURRENT: LocalData = const { LocalData {
     ctx: RcCell::new(),
+    wake_on_schedule: Cell::new(false),
 } });
 
 struct LocalData {
     ctx: RcCell<Context>,
+    wake_on_schedule: Cell<bool>,
+}
+
+impl LocalData {
+    /// Should be called except when we call `LocalSet::enter`.
+    /// Especially when we poll a LocalSet.
+    #[must_use = "dropping this guard will reset the entered state"]
+    fn enter(&self, ctx: Rc<Context>) -> LocalDataEnterGuard<'_> {
+        let ctx = self.ctx.replace(Some(ctx));
+        let wake_on_schedule = self.wake_on_schedule.replace(false);
+        LocalDataEnterGuard {
+            local_data_ref: self,
+            ctx,
+            wake_on_schedule,
+        }
+    }
+}
+
+/// A guard for `LocalData::enter()`
+struct LocalDataEnterGuard<'a> {
+    local_data_ref: &'a LocalData,
+    ctx: Option<Rc<Context>>,
+    wake_on_schedule: bool,
+}
+
+impl<'a> Drop for LocalDataEnterGuard<'a> {
+    fn drop(&mut self) {
+        self.local_data_ref.ctx.set(self.ctx.take());
+        self.local_data_ref
+            .wake_on_schedule
+            .set(self.wake_on_schedule)
+    }
 }
 
 cfg_rt! {
@@ -360,13 +393,26 @@ const MAX_TASKS_PER_TICK: usize = 61;
 const REMOTE_FIRST_INTERVAL: u8 = 31;
 
 /// Context guard for LocalSet
-pub struct LocalEnterGuard(Option<Rc<Context>>);
+pub struct LocalEnterGuard {
+    ctx: Option<Rc<Context>>,
+
+    /// Distinguishes whether the context was entered or being polled.
+    /// When we enter it, the value `wake_on_schedule` is set. In this case
+    /// `spawn_local` refers the context, whereas it is not being polled now.
+    wake_on_schedule: bool,
+}
 
 impl Drop for LocalEnterGuard {
     fn drop(&mut self) {
-        CURRENT.with(|LocalData { ctx, .. }| {
-            ctx.set(self.0.take());
-        })
+        CURRENT.with(
+            |LocalData {
+                 ctx,
+                 wake_on_schedule,
+             }| {
+                ctx.set(self.ctx.take());
+                wake_on_schedule.set(self.wake_on_schedule);
+            },
+        )
     }
 }
 
@@ -408,10 +454,20 @@ impl LocalSet {
     ///
     /// [`spawn_local`]: fn@crate::task::spawn_local
     pub fn enter(&self) -> LocalEnterGuard {
-        CURRENT.with(|LocalData { ctx, .. }| {
-            let old = ctx.replace(Some(self.context.clone()));
-            LocalEnterGuard(old)
-        })
+        CURRENT.with(
+            |LocalData {
+                 ctx,
+                 wake_on_schedule,
+                 ..
+             }| {
+                let ctx = ctx.replace(Some(self.context.clone()));
+                let wake_on_schedule = wake_on_schedule.replace(true);
+                LocalEnterGuard {
+                    ctx,
+                    wake_on_schedule,
+                }
+            },
+        )
     }
 
     /// Spawns a `!Send` task onto the local task set.
@@ -667,23 +723,8 @@ impl LocalSet {
     }
 
     fn with<T>(&self, f: impl FnOnce() -> T) -> T {
-        CURRENT.with(|LocalData { ctx, .. }| {
-            struct Reset<'a> {
-                ctx_ref: &'a RcCell<Context>,
-                val: Option<Rc<Context>>,
-            }
-            impl<'a> Drop for Reset<'a> {
-                fn drop(&mut self) {
-                    self.ctx_ref.set(self.val.take());
-                }
-            }
-            let old = ctx.replace(Some(self.context.clone()));
-
-            let _reset = Reset {
-                ctx_ref: ctx,
-                val: old,
-            };
-
+        CURRENT.with(|local_data| {
+            let _guard = local_data.enter(self.context.clone());
             f()
         })
     }
@@ -693,23 +734,8 @@ impl LocalSet {
     fn with_if_possible<T>(&self, f: impl FnOnce() -> T) -> T {
         let mut f = Some(f);
 
-        let res = CURRENT.try_with(|LocalData { ctx, .. }| {
-            struct Reset<'a> {
-                ctx_ref: &'a RcCell<Context>,
-                val: Option<Rc<Context>>,
-            }
-            impl<'a> Drop for Reset<'a> {
-                fn drop(&mut self) {
-                    self.ctx_ref.replace(self.val.take());
-                }
-            }
-            let old = ctx.replace(Some(self.context.clone()));
-
-            let _reset = Reset {
-                ctx_ref: ctx,
-                val: old,
-            };
-
+        let res = CURRENT.try_with(|local_data| {
+            let _guard = local_data.enter(self.context.clone());
             (f.take().unwrap())()
         });
 
@@ -967,7 +993,10 @@ impl Shared {
     fn schedule(&self, task: task::Notified<Arc<Self>>) {
         CURRENT.with(|localdata| {
             match localdata.ctx.get() {
-                Some(cx) if cx.shared.ptr_eq(self) => unsafe {
+                // If the current `LocalSet` is being polled, we don't need to wake it.
+                // When we `enter` it, then the value `wake_on_schedule` is set to be true.
+                // In this case it is not being polled, so we need to wake it.
+                Some(cx) if cx.shared.ptr_eq(self) && !localdata.wake_on_schedule.get() => unsafe {
                     // Safety: if the current `LocalSet` context points to this
                     // `LocalSet`, then we are on the thread that owns it.
                     cx.shared.local_state.task_push_back(task);
diff --git a/tokio/tests/task_local_set.rs b/tokio/tests/task_local_set.rs
index baca58b77..168a05808 100644
--- a/tokio/tests/task_local_set.rs
+++ b/tokio/tests/task_local_set.rs
@@ -573,6 +573,27 @@ async fn spawn_wakes_localset() {
     }
 }
 
+/// Checks that the task wakes up with `enter`.
+/// Reproduces <https://github.com/tokio-rs/tokio/issues/5020>.
+#[tokio::test]
+async fn sleep_with_local_enter_guard() {
+    let local = LocalSet::new();
+    let _guard = local.enter();
+
+    let (tx, rx) = oneshot::channel();
+
+    local
+        .run_until(async move {
+            tokio::task::spawn_local(async move {
+                time::sleep(Duration::ZERO).await;
+
+                tx.send(()).expect("failed to send");
+            });
+            assert_eq!(rx.await, Ok(()));
+        })
+        .await;
+}
+
 #[test]
 fn store_local_set_in_thread_local_with_runtime() {
     use tokio::runtime::Runtime;