diff --git a/packages/flutter/lib/src/material/tooltip.dart b/packages/flutter/lib/src/material/tooltip.dart
index 6fb42527111c..c0ea84ce6663 100644
--- a/packages/flutter/lib/src/material/tooltip.dart
+++ b/packages/flutter/lib/src/material/tooltip.dart
@@ -665,19 +665,18 @@ class TooltipState extends State<Tooltip> with SingleTickerProviderStateMixin {
     // tooltip is the first to be hit in the widget tree's hit testing order.
     // See also _ExclusiveMouseRegion for the exact behavior.
     _activeHoveringPointerDevices.add(event.device);
-    final List<TooltipState> openedTooltips = Tooltip._openedTooltips.toList();
-    bool otherTooltipsDismissed = false;
-    for (final TooltipState tooltip in openedTooltips) {
+    // Dismiss other open tooltips unless they're kept visible by other mice.
+    // The mouse tracker implementation always dispatches all `onExit` events
+    // before dispatching any `onEnter` events, so `event.device` must have
+    // already been removed from _activeHoveringPointerDevices of the tooltips
+    // that are no longer being hovered over.
+    final List<TooltipState> tooltipsToDismiss = Tooltip._openedTooltips
+      .where((TooltipState tooltip) => tooltip._activeHoveringPointerDevices.isEmpty).toList();
+    for (final TooltipState tooltip in tooltipsToDismiss) {
       assert(tooltip.mounted);
-      final Set<int> hoveringDevices = tooltip._activeHoveringPointerDevices;
-      final bool shouldDismiss = tooltip != this
-                              && (hoveringDevices.length == 1 && hoveringDevices.single == event.device);
-      if (shouldDismiss) {
-        otherTooltipsDismissed = true;
-        tooltip._scheduleDismissTooltip(withDelay: Duration.zero);
-      }
+      tooltip._scheduleDismissTooltip(withDelay: Duration.zero);
     }
-    _scheduleShowTooltip(withDelay: otherTooltipsDismissed ? Duration.zero : _waitDuration);
+    _scheduleShowTooltip(withDelay: tooltipsToDismiss.isNotEmpty ? Duration.zero : _waitDuration);
   }
 
   void _handleMouseExit(PointerExitEvent event) {
diff --git a/packages/flutter/test/material/tooltip_test.dart b/packages/flutter/test/material/tooltip_test.dart
index c9849c070ab6..76e5fc7524a3 100644
--- a/packages/flutter/test/material/tooltip_test.dart
+++ b/packages/flutter/test/material/tooltip_test.dart
@@ -1508,6 +1508,60 @@ void main() {
     expect(find.text(tooltipText), findsNothing);
   });
 
+  // Regression test for https://github.com/flutter/flutter/issues/141644.
+  // This allows the user to quickly explore the UI via tooltips.
+  testWidgets('Tooltip shows without delay when the mouse moves from another tooltip', (WidgetTester tester) async {
+    const Duration waitDuration = Durations.extralong1;
+    final TestGesture gesture = await tester.createGesture(kind: PointerDeviceKind.mouse);
+    addTearDown(() async {
+      return gesture.removePointer();
+    });
+    await gesture.addPointer();
+    await gesture.moveTo(const Offset(1.0, 1.0));
+    await tester.pump();
+    await gesture.moveTo(Offset.zero);
+
+    await tester.pumpWidget(
+      const MaterialApp(
+        home: Column(
+          children: <Widget>[
+            Tooltip(
+              message: 'first tooltip',
+              waitDuration: waitDuration,
+              child: SizedBox(
+                width: 100.0,
+                height: 100.0,
+              ),
+            ),
+            Tooltip(
+              message: 'last tooltip',
+              waitDuration: waitDuration,
+              child: SizedBox(
+                width: 100.0,
+                height: 100.0,
+              ),
+            ),
+          ],
+        ),
+      ),
+    );
+
+    await gesture.moveTo(Offset.zero);
+    await tester.pump();
+    await gesture.moveTo(tester.getCenter(find.byType(Tooltip).first));
+    await tester.pump();
+    // Wait for the first tooltip to appear.
+    await tester.pump(waitDuration);
+    expect(find.text('first tooltip'), findsOneWidget);
+    expect(find.text('last tooltip'), findsNothing);
+
+    // Move to the second tooltip and expect it to show up immediately.
+    await gesture.moveTo(tester.getCenter(find.byType(Tooltip).last));
+    await tester.pump();
+    expect(find.text('first tooltip'), findsNothing);
+    expect(find.text('last tooltip'), findsOneWidget);
+  });
+
   testWidgets('Tooltip text is also hoverable', (WidgetTester tester) async {
     const Duration waitDuration = Duration.zero;
     final TestGesture gesture = await tester.createGesture(kind: PointerDeviceKind.mouse);