diff --git a/starlette/middleware/http.py b/starlette/middleware/http.py
index aa1675263..76298e4d1 100644
--- a/starlette/middleware/http.py
+++ b/starlette/middleware/http.py
@@ -66,9 +66,10 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
                 return
 
             response_started = False
+            response_finished = False
 
             async def wrapped_send(message: Message) -> None:
-                nonlocal response_started
+                nonlocal response_started, response_finished
 
                 if message["type"] == "http.response.start":
                     response_started = True
@@ -77,17 +78,27 @@ async def wrapped_send(message: Message) -> None:
                     response.raw_headers.clear()
 
                     try:
-                        await flow.asend(response)
+                        new_response = await flow.asend(response)
                     except StopAsyncIteration:
                         pass
                     else:
-                        raise RuntimeError("dispatch() should yield exactly once")
-
+                        if new_response is None:
+                            raise RuntimeError("dispatch() should yield exactly once")
+                        try:
+                            await flow.__anext__()
+                        except StopAsyncIteration:
+                            pass
+                        else:
+                            raise RuntimeError("dispatch() should yield exactly once")
+                        await new_response(scope, receive, send)
+                        response_finished = True
+                        return
                     headers = MutableHeaders(raw=message["headers"])
                     headers.update(response.headers)
                     message["headers"] = headers.raw
 
-                await send(message)
+                if not response_finished:
+                    await send(message)
 
             try:
                 await self.app(scope, receive, wrapped_send)
diff --git a/tests/middleware/test_http.py b/tests/middleware/test_http.py
index cbe1c3ac7..1add61fcf 100644
--- a/tests/middleware/test_http.py
+++ b/tests/middleware/test_http.py
@@ -169,6 +169,79 @@ async def dispatch(
         client.get("/")
 
 
+def test_replace_response(test_client_factory: Callable[[ASGIApp], TestClient]) -> None:
+    async def index(request: Request) -> Response:
+        return PlainTextResponse("Hello, world!")
+
+    class CustomMiddleware(HTTPMiddleware):
+        async def dispatch(
+            self, conn: HTTPConnection
+        ) -> AsyncGenerator[Optional[Response], Response]:
+            yield None
+            yield PlainTextResponse("Custom")
+
+    app = Starlette(
+        routes=[Route("/", index)],
+        middleware=[Middleware(CustomMiddleware)],
+    )
+
+    client = test_client_factory(app)
+
+    resp = client.get("/")
+    assert resp.text == "Custom"
+
+
+def test_replace_response_too_many_yields(
+    test_client_factory: Callable[[ASGIApp], TestClient]
+) -> None:
+    async def index(request: Request) -> Response:
+        return PlainTextResponse("Hello, world!")
+
+    class CustomMiddleware(HTTPMiddleware):
+        async def dispatch(
+            self, conn: HTTPConnection
+        ) -> AsyncGenerator[Optional[Response], Response]:
+            yield None
+            yield PlainTextResponse("Custom")
+            yield None
+
+    app = Starlette(
+        routes=[Route("/", index)],
+        middleware=[Middleware(CustomMiddleware)],
+    )
+
+    client = test_client_factory(app)
+
+    client = test_client_factory(app)
+    with pytest.raises(RuntimeError, match="should yield exactly once"):
+        client.get("/")
+
+
+def test_replace_response_yield_None(
+    test_client_factory: Callable[[ASGIApp], TestClient]
+) -> None:
+    async def index(request: Request) -> Response:
+        return PlainTextResponse("Hello, world!")
+
+    class CustomMiddleware(HTTPMiddleware):
+        async def dispatch(
+            self, conn: HTTPConnection
+        ) -> AsyncGenerator[Optional[Response], Response]:
+            yield None
+            yield None
+
+    app = Starlette(
+        routes=[Route("/", index)],
+        middleware=[Middleware(CustomMiddleware)],
+    )
+
+    client = test_client_factory(app)
+
+    client = test_client_factory(app)
+    with pytest.raises(RuntimeError, match="should yield exactly once"):
+        client.get("/")
+
+
 def test_error_response(test_client_factory: Callable[[ASGIApp], TestClient]) -> None:
     class Failed(Exception):
         pass