diff --git a/CHANGELOG.md b/CHANGELOG.md
index 072f92175e..f3a334e35c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,8 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 
 - Fixed `VERTICAL_BREAKPOINTS` doesn't work https://github.com/Textualize/textual/pull/5785
 - Fixed `Button` allowing text selection https://github.com/Textualize/textual/pull/5770
+- Fixed running `App.run` after `asyncio.run` https://github.com/Textualize/textual/pull/5799
+- Fixed triggering a deprecation warning in py >= 3.10 https://github.com/Textualize/textual/pull/5799
 
 ## [3.2.0] - 2025-05-02
 
diff --git a/src/textual/app.py b/src/textual/app.py
index 9ae50e7421..332e9ff13f 100644
--- a/src/textual/app.py
+++ b/src/textual/app.py
@@ -150,6 +150,9 @@
 if constants.DEBUG:
     warnings.simplefilter("always", ResourceWarning)
 
+# `asyncio.get_event_loop()` is deprecated since Python 3.10:
+_ASYNCIO_GET_EVENT_LOOP_IS_DEPRECATED = sys.version_info >= (3, 10, 0)
+
 ComposeResult = Iterable[Widget]
 RenderResult: TypeAlias = "RenderableType | Visual | SupportsVisual"
 """Result of Widget.render()"""
@@ -2140,9 +2143,9 @@ def run(
             App return value.
         """
 
-        async def run_app() -> None:
+        async def run_app() -> ReturnType | None:
             """Run the app."""
-            await self.run_async(
+            return await self.run_async(
                 headless=headless,
                 inline=inline,
                 inline_no_clear=inline_no_clear,
@@ -2151,9 +2154,24 @@ async def run_app() -> None:
                 auto_pilot=auto_pilot,
             )
 
-        event_loop = asyncio.get_event_loop() if loop is None else loop
-        event_loop.run_until_complete(run_app())
-        return self.return_value
+        if loop is None:
+            if _ASYNCIO_GET_EVENT_LOOP_IS_DEPRECATED:
+                # N.B. This does work with Python<3.10, but global Locks, Events, etc
+                # eagerly bind the event loop, and result in Future bound to wrong
+                # loop errors.
+                return asyncio.run(run_app())
+            try:
+                global_loop = asyncio.get_event_loop()
+            except RuntimeError:
+                # the global event loop may have been destroyed by someone running
+                # asyncio.run(), or asyncio.set_event_loop(None), in which case
+                # we need to use asyncio.run() also. (We run this outside the
+                # context of an exception handler)
+                pass
+            else:
+                return global_loop.run_until_complete(run_app())
+            return asyncio.run(run_app())
+        return loop.run_until_complete(run_app())
 
     async def _on_css_change(self) -> None:
         """Callback for the file monitor, called when CSS files change."""
diff --git a/tests/test_app.py b/tests/test_app.py
index 782b99e671..3c6d54aed8 100644
--- a/tests/test_app.py
+++ b/tests/test_app.py
@@ -367,3 +367,20 @@ def on_mount(self) -> None:
     app = MyApp()
     result = await app.run_async()
     assert result == 42
+
+
+def test_app_loop_run_after_asyncio_run() -> None:
+    """Test that App.run runs after asyncio.run has run."""
+
+    class MyApp(App[int]):
+        def on_mount(self) -> None:
+            self.exit(42)
+
+    async def amain():
+        pass
+
+    asyncio.run(amain())
+
+    app = MyApp()
+    result = app.run()
+    assert result == 42