Gordon, filling in for Marshall Faulk, who is out at least a month with a broken left hand, made an immediate impact, capping an eight-play, 46-yard game-opening drive with a three-yard touchdown run.
Isaac Bruce caught four passes for 58 yards to pass Henry Ellard for the Rams' all-time receiving record with 9,790 yards.
Emmitt Smith scored his first touchdown as a Cardinal, a one-yard run on 4th-and-goal with 36 seconds left in the second quarter. Josh Scoey had a 100-yard kickoff return for Arizona (1-3).
The Cardinals had upset Green Bay, 20-13, last week.