diff --git a/datasette/utils/asgi.py b/datasette/utils/asgi.py
index 2d4a6cf..0bf7ca1 100644
--- a/datasette/utils/asgi.py
+++ b/datasette/utils/asgi.py
@@ -123,16 +123,30 @@ class Request:
     def scheme(self):
         return self.scope.get("scheme") or "http"
 
+    # Decoded headers are cached against a snapshot of the raw scope headers
+    # they came from, so they stay correct if request.scope is replaced (as
+    # DatasetteRouter.route_path does) or scope["headers"] is modified
+    _raw_headers = None
+    _decoded_headers = None
+
+    def _headers(self):
+        raw_headers = list(self.scope.get("headers") or [])
+        if self._decoded_headers is None or raw_headers != self._raw_headers:
+            self._decoded_headers = _RequestHeaders(
+                (k.decode("latin-1").lower(), v.decode("latin-1"))
+                for k, v in raw_headers
+            )
+            self._raw_headers = raw_headers
+        return self._decoded_headers
+
     @property
     def headers(self):
-        return _RequestHeaders(
-            (k.decode("latin-1").lower(), v.decode("latin-1"))
-            for k, v in self.scope.get("headers") or []
-        )
+        # A copy, so callers cannot modify the cached headers
+        return _RequestHeaders(self._headers())
 
     @property
     def host(self):
-        return self.headers.get("host") or "localhost"
+        return self._headers().get("host") or "localhost"
 
     @property
     def cookies(self):
diff --git a/tests/test_internals_request.py b/tests/test_internals_request.py
index 91ef368..f1ef381 100644
--- a/tests/test_internals_request.py
+++ b/tests/test_internals_request.py
@@ -80,6 +80,25 @@ def test_request_headers_missing(scope):
         headers["Content-Type"]
 
 
+def test_request_headers_follow_scope_changes():
+    scope = {"headers": [(b"host", b"example.com"), (b"x-one", b"1")]}
+    request = Request(scope, None)
+    headers = request.headers
+    assert headers == {"host": "example.com", "x-one": "1"}
+    # Modifying the returned headers does not affect later lookups
+    headers["x-one"] = "changed"
+    assert request.headers["x-one"] == "1"
+    # Replacing request.scope, as DatasetteRouter.route_path does
+    request.scope = dict(scope, headers=[(b"host", b"other.com")])
+    assert request.headers == {"host": "other.com"}
+    assert request.host == "other.com"
+    # Modifying scope["headers"] in place
+    request.scope["headers"].append((b"x-two", b"2"))
+    assert request.headers == {"host": "other.com", "x-two": "2"}
+    request.scope["headers"][0] = (b"host", b"third.com")
+    assert request.host == "third.com"
+
+
 @pytest.mark.asyncio
 async def test_request_post_vars():
     scope = {