Both sides struggled for consistency in a first half lacking star quality, with Jay Feely edging the Cardinals ahead with two perfectly-placed field goals.
The second half saw the Cardinals step things up and score 18 answered points to pull away as Cam Newton failed to inspire the Panthers.
Midway through the third quarter Arizona got the game's first touchdown after a sustained drive upfield by Palmer, with Rashard Mendenhall finishing from close range to get the important score.
Newton was then sacked in the end zone as he attempted to respond just 30 seconds later by Calais Campbell, allowing the Cards to pick up two more points for the safety.
Feely's 50-yard field goal pushed the Cardinals further ahead in the fourth quarter, before Palmer found Jim Dray with seven-yard touchdown pass two minutes from time to make sure of a home win for Arizona.