diff --git a/src/requests/auth.py b/src/requests/auth.py
index 4a7ce6dc14..bbe1c153d5 100644
--- a/src/requests/auth.py
+++ b/src/requests/auth.py
@@ -225,11 +225,11 @@ def sha512_utf8(x):
         if opaque:
             base += f', opaque="{opaque}"'
         if algorithm:
-            base += f', algorithm="{algorithm}"'
+            base += f', algorithm={algorithm}'
         if entdig:
             base += f', digest="{entdig}"'
         if qop:
-            base += f', qop="auth", nc={ncvalue}, cnonce="{cnonce}"'
+            base += f', qop=auth, nc={ncvalue}, cnonce="{cnonce}"'
 
         return f"Digest {base}"
 
diff --git a/tests/test_requests.py b/tests/test_requests.py
index 75d2deff2e..08e0b75e37 100644
--- a/tests/test_requests.py
+++ b/tests/test_requests.py
@@ -797,13 +797,19 @@ def test_DIGESTAUTH_WRONG_HTTP_401_GET(self, httpbin):
             r = s.get(url)
             assert r.status_code == 401
 
-    def test_DIGESTAUTH_QUOTES_QOP_VALUE(self, httpbin):
+    def test_DIGESTAUTH_NO_QUOTES_QOP_ALGORITHM_NC_VALUES(self, httpbin):
+        """RFC7616 states the following for the Authentication header:
+        "For historical reasons, a sender MUST NOT generate the quoted string
+        syntax for the following parameters: algorithm, qop, and nc."
+        """
         for authtype in self.digest_auth_algo:
             auth = HTTPDigestAuth("user", "pass")
             url = httpbin("digest-auth", "auth", "user", "pass", authtype)
 
             r = requests.get(url, auth=auth)
-            assert '"auth"' in r.request.headers["Authorization"]
+            assert ' qop=auth,' in r.request.headers["Authorization"]
+            assert f' algorithm={authtype},' in r.request.headers["Authorization"]
+            assert re.search(r' nc=[0-9]+,', r.request.headers["Authorization"])
 
     def test_POSTBIN_GET_POST_FILES(self, httpbin):
         url = httpbin("post")