diff --git a/Lib/unittest/async_case.py b/Lib/unittest/async_case.py
index 1bc1312c8c2ee9..520213c3727555 100644
--- a/Lib/unittest/async_case.py
+++ b/Lib/unittest/async_case.py
@@ -102,9 +102,9 @@ async def _asyncioLoopRunner(self, fut):
                 ret = await awaitable
                 if not fut.cancelled():
                     fut.set_result(ret)
-            except asyncio.CancelledError:
+            except (SystemExit, KeyboardInterrupt):
                 raise
-            except Exception as ex:
+            except (BaseException, asyncio.CancelledError) as ex:
                 if not fut.cancelled():
                     fut.set_exception(ex)
 
diff --git a/Lib/unittest/test/test_async_case.py b/Lib/unittest/test/test_async_case.py
index 2db441da202a01..d01864b6936ca8 100644
--- a/Lib/unittest/test/test_async_case.py
+++ b/Lib/unittest/test/test_async_case.py
@@ -190,6 +190,33 @@ async def on_async_cleanup(self, val):
                                   'async_cleanup 2',
                                   'sync_cleanup 1'])
 
+    def test_base_exception_from_async_method(self):
+        events = []
+        class Test(unittest.IsolatedAsyncioTestCase):
+            async def test_base(self):
+                events.append("test_base")
+                raise BaseException()
+                events.append("not it")
+
+            async def test_no_err(self):
+                events.append("test_no_err")
+
+            async def test_cancel(self):
+                raise asyncio.CancelledError()
+
+        test = Test("test_base")
+        output = test.run()
+        self.assertFalse(output.wasSuccessful())
+
+        test = Test("test_no_err")
+        test.run()
+        self.assertEqual(events, ['test_base', 'test_no_err'])
+
+        test = Test("test_cancel")
+        output = test.run()
+        self.assertFalse(output.wasSuccessful())
+
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Misc/NEWS.d/next/Library/2020-10-11-21-43-03.bpo-39101.-I49Pm.rst b/Misc/NEWS.d/next/Library/2020-10-11-21-43-03.bpo-39101.-I49Pm.rst
new file mode 100644
index 00000000000000..a571e8343cde12
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-10-11-21-43-03.bpo-39101.-I49Pm.rst
@@ -0,0 +1 @@
+Fixed tests using IsolatedAsyncioTestCase from hanging on BaseExceptions.
\ No newline at end of file