Palmer made good on 27-of-32 passes, including a 7-yard TD strike to Fitzgerald in the second quarter, as the Cardinals (8-5) notched a fifth win in six games.
Fitzgerald finished with 12 grabs for 96 yards.
Rashard Mendenhall and Andre Ellington each added a rushing touchdown for Arizona.
The Rams (5-8) lost for the fifth time in seven contests as Kellen Clemens was intercepted twice. He was held to 181 aerial yards on 16-for-27 efficiency.