diff --git a/rest_framework/compat.py b/rest_framework/compat.py
index 080816094..5924d4651 100644
--- a/rest_framework/compat.py
+++ b/rest_framework/compat.py
@@ -41,8 +41,8 @@ except ImportError:
     uritemplate = None
 
 
-# async_to_sync is required for async View support
-if django.VERSION >= (3, 1):
+# async_to_sync is required for async view support
+if django.VERSION >= (4, 1):
     from asgiref.sync import async_to_sync
 else:
     async_to_sync = None
diff --git a/rest_framework/views.py b/rest_framework/views.py
index 96591d591..f30da98d3 100644
--- a/rest_framework/views.py
+++ b/rest_framework/views.py
@@ -14,7 +14,6 @@ from django.views.decorators.csrf import csrf_exempt
 from django.views.generic import View
 
 from rest_framework import exceptions, status
-from rest_framework.compat import async_to_sync
 from rest_framework.request import Request
 from rest_framework.response import Response
 from rest_framework.schemas import DefaultSchema
@@ -506,12 +505,7 @@ class APIView(View):
             else:
                 handler = self.http_method_not_allowed
 
-            if asyncio.iscoroutinefunction(handler):
-                if not async_to_sync:
-                    raise Exception('Async API views are supported only for django>=3.1.')
-                response = async_to_sync(handler)(request, *args, **kwargs)
-            else:
-                response = handler(request, *args, **kwargs)
+            response = handler(request, *args, **kwargs)
 
         except Exception as exc:
             response = self.handle_exception(exc)
@@ -527,3 +521,37 @@ class APIView(View):
             return self.http_method_not_allowed(request, *args, **kwargs)
         data = self.metadata_class().determine_metadata(request, self)
         return Response(data, status=status.HTTP_200_OK)
+
+
+class AsyncAPIView(APIView):
+    async def dispatch(self, request, *args, **kwargs):
+        """
+        `.dispatch()` is pretty much the same as Django's regular dispatch,
+        but with extra hooks for startup, finalize, and exception handling.
+        """
+        self.args = args
+        self.kwargs = kwargs
+        request = self.initialize_request(request, *args, **kwargs)
+        self.request = request
+        self.headers = self.default_response_headers  # deprecate?
+
+        try:
+            self.initial(request, *args, **kwargs)
+
+            # Get the appropriate handler method
+            if request.method.lower() in self.http_method_names:
+                handler = getattr(self, request.method.lower(),
+                                  self.http_method_not_allowed)
+            else:
+                handler = self.http_method_not_allowed
+
+            if asyncio.iscoroutinefunction(handler):
+                response = await handler(request, *args, **kwargs)
+            else:
+                raise Exception('Async methods should be used on an async view.')
+
+        except Exception as exc:
+            response = self.handle_exception(exc)
+
+        self.response = self.finalize_response(request, response, *args, **kwargs)
+        return self.response
diff --git a/tests/test_views.py b/tests/test_views.py
index 61d073270..64fceb0d6 100644
--- a/tests/test_views.py
+++ b/tests/test_views.py
@@ -5,11 +5,12 @@ import pytest
 from django.test import TestCase
 
 from rest_framework import status
+from rest_framework.compat import async_to_sync
 from rest_framework.decorators import api_view
 from rest_framework.response import Response
 from rest_framework.settings import APISettings, api_settings
 from rest_framework.test import APIRequestFactory
-from rest_framework.views import APIView
+from rest_framework.views import APIView, AsyncAPIView
 
 factory = APIRequestFactory()
 
@@ -24,7 +25,7 @@ class BasicView(APIView):
         return Response({'method': 'POST', 'data': request.data})
 
 
-class BasicAsyncView(APIView):
+class BasicAsyncView(AsyncAPIView):
     async def get(self, request, *args, **kwargs):
         return Response({'method': 'GET'})
 
@@ -139,8 +140,8 @@ class FunctionBasedViewIntegrationTests(TestCase):
 
 
 @pytest.mark.skipif(
-    django.VERSION < (3, 1),
-    reason="Async view support requires Django 3.1 or higher",
+    django.VERSION < (4, 1),
+    reason="Async view support requires Django 4.1 or higher",
 )
 class ClassBasedAsyncViewIntegrationTests(TestCase):
     def setUp(self):
@@ -148,13 +149,13 @@ class ClassBasedAsyncViewIntegrationTests(TestCase):
 
     def test_get_succeeds(self):
         request = factory.get('/')
-        response = self.view(request)
+        response = async_to_sync(self.view)(request)
         assert response.status_code == status.HTTP_200_OK
         assert response.data == {'method': 'GET'}
 
     def test_post_succeeds(self):
         request = factory.post('/', {'test': 'foo'})
-        response = self.view(request)
+        response = async_to_sync(self.view)(request)
         expected = {
             'method': 'POST',
             'data': {'test': ['foo']}
@@ -164,7 +165,7 @@ class ClassBasedAsyncViewIntegrationTests(TestCase):
 
     def test_400_parse_error(self):
         request = factory.post('/', 'f00bar', content_type='application/json')
-        response = self.view(request)
+        response = async_to_sync(self.view)(request)
         expected = {
             'detail': JSON_ERROR
         }