diff --git a/src/engineio/async_drivers/asgi.py b/src/engineio/async_drivers/asgi.py
index cd1dd0e..bd50226 100644
--- a/src/engineio/async_drivers/asgi.py
+++ b/src/engineio/async_drivers/asgi.py
@@ -63,7 +63,8 @@ async def __call__(self, scope, receive, send):
             await self.lifespan(scope, receive, send)
         elif scope['type'] in ['http', 'websocket'] and (
                 self.engineio_path is None
-                or scope['path'].startswith(self.engineio_path)):
+                or self._ensure_trailing_slash(scope['path']).startswith(
+                    self.engineio_path)):
             await self.engineio_server.handle_request(scope, receive, send)
         else:
             static_file = get_static_file(scope['path'], self.static_files) \
@@ -127,6 +128,11 @@ async def not_found(self, receive, send):
         await send({'type': 'http.response.body',
                     'body': b'Not Found'})
 
+    def _ensure_trailing_slash(self, path):
+        if not path.endswith('/'):
+            path += '/'
+        return path
+
 
 async def translate_request(scope, receive, send):
     class AwaitablePayload(object):  # pragma: no cover
diff --git a/tests/async/test_asgi.py b/tests/async/test_asgi.py
index 62a6447..d45b63c 100644
--- a/tests/async/test_asgi.py
+++ b/tests/async/test_asgi.py
@@ -38,12 +38,55 @@ def test_create_app(self):
     def test_engineio_routing(self):
         mock_server = mock.MagicMock()
         mock_server.handle_request = AsyncMock()
+
         app = async_asgi.ASGIApp(mock_server)
         scope = {'type': 'http', 'path': '/engine.io/'}
         _run(app(scope, 'receive', 'send'))
         mock_server.handle_request.mock.assert_called_once_with(
             scope, 'receive', 'send'
         )
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/engine.io/'}
+        _run(app(scope, 'receive', 'send'))
+        mock_server.handle_request.mock.assert_called_once_with(
+            scope, 'receive', 'send'
+        )
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/engine.iofoo/'}
+        _run(app(scope, 'receive', AsyncMock()))
+        mock_server.handle_request.mock.assert_not_called()
+
+        app = async_asgi.ASGIApp(mock_server, engineio_path=None)
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/foo'}
+        _run(app(scope, 'receive', 'send'))
+        mock_server.handle_request.mock.assert_called_once_with(
+            scope, 'receive', 'send'
+        )
+
+        app = async_asgi.ASGIApp(mock_server, engineio_path='mysocket.io')
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/mysocket.io'}
+        _run(app(scope, 'receive', 'send'))
+        mock_server.handle_request.mock.assert_called_once_with(
+            scope, 'receive', 'send'
+        )
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/mysocket.io/'}
+        _run(app(scope, 'receive', 'send'))
+        mock_server.handle_request.mock.assert_called_once_with(
+            scope, 'receive', 'send'
+        )
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/mysocket.io/foo'}
+        _run(app(scope, 'receive', 'send'))
+        mock_server.handle_request.mock.assert_called_once_with(
+            scope, 'receive', 'send'
+        )
+        mock_server.handle_request.mock.reset_mock()
+        scope = {'type': 'http', 'path': '/mysocket.iofoo'}
+        _run(app(scope, 'receive', AsyncMock()))
+        mock_server.handle_request.mock.assert_not_called()
 
     def test_other_app_routing(self):
         other_app = AsyncMock()