diff --git a/starlette/routing.py b/starlette/routing.py
index 1aa2cdb6d..7253321cc 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -234,7 +234,11 @@ def __init__(
 
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
         if scope["type"] == "http":
-            match = self.path_regex.match(scope["path"])
+            root_path = scope.get("current_root_path", scope.get("root_path", ""))
+            path = scope.get(
+                "current_path", re.sub(r"^" + root_path, "", scope["path"])
+            )
+            match = self.path_regex.match(path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
@@ -370,21 +374,25 @@ def routes(self) -> typing.List[BaseRoute]:
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
         if scope["type"] in ("http", "websocket"):
             path = scope["path"]
-            match = self.path_regex.match(path)
+            root_path = scope.get("current_root_path", scope.get("root_path", ""))
+            current_path = scope.get("current_path", re.sub(r"^" + root_path, "", path))
+            match = self.path_regex.match(current_path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
                     matched_params[key] = self.param_convertors[key].convert(value)
                 remaining_path = "/" + matched_params.pop("path")
-                matched_path = path[: -len(remaining_path)]
+                matched_path = current_path[: -len(remaining_path)]
                 path_params = dict(scope.get("path_params", {}))
                 path_params.update(matched_params)
                 root_path = scope.get("root_path", "")
                 child_scope = {
                     "path_params": path_params,
                     "app_root_path": scope.get("app_root_path", root_path),
-                    "root_path": root_path + matched_path,
-                    "path": remaining_path,
+                    "current_root_path": root_path + matched_path,
+                    "current_path": remaining_path,
+                    "root_path": root_path,
+                    "path": path,
                     "endpoint": self.app,
                 }
                 return Match.FULL, child_scope
diff --git a/tests/test_routing.py b/tests/test_routing.py
index e3b1e412a..3b7cf54da 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -549,6 +549,60 @@ def test_url_for_with_root_path(test_client_factory):
     }
 
 
+async def echo_paths(request, name):
+    return JSONResponse(
+        {
+            "name": name,
+            "path": request.scope["path"],
+            "root_path": request.scope["root_path"],
+        }
+    )
+
+
+echo_paths_routes = [
+    Route(
+        "/path",
+        functools.partial(echo_paths, name="path"),
+        name="path",
+        methods=["GET"],
+    ),
+    Mount(
+        "/root",
+        name="mount",
+        routes=[
+            Route(
+                "/path",
+                functools.partial(echo_paths, name="subpath"),
+                name="subpath",
+                methods=["GET"],
+            )
+        ],
+    ),
+]
+
+
+def test_paths_with_root_path(test_client_factory):
+    app = Starlette(routes=echo_paths_routes)
+    client = test_client_factory(
+        app, base_url="https://www.example.org/", root_path="/root"
+    )
+    response = client.get("/root/path")
+    assert response.status_code == 200
+    assert response.json() == {
+        "name": "path",
+        "path": "/root/path",
+        "root_path": "/root",
+    }
+
+    response = client.get("/root/root/path")
+    assert response.status_code == 200
+    assert response.json() == {
+        "name": "subpath",
+        "path": "/root/root/path",
+        "root_path": "/root",
+    }
+
+
 async def stub_app(scope, receive, send):
     pass  # pragma: no cover