Marco Wilson and Isaiah Simmons scored touchdowns on two pick-sixes late in the first half, putting the Cardinals in control.
The Saints pulled within 28-17 early in the third, but Kyler Murray found Greg Dortch for a five-yard touchdown pass to push Arizona ahead 35-17.
Murray completed 20 of 29 passes for 204 yards and a touchdown.
New Orleans (2-5) has lost five of its last six games. Andy Dalton threw for 361 yards, four touchdowns and three interceptions.
The Saints led 7-3 late in the first quarter and looked as if they were going to score another touchdown, but Cardinals cornerback Antonio Hamilton intercepted Dalton's pass in the end zone.
New Orleans did push ahead 14-6 in the second on a three-yard touchdown pass to Taysom Hill. The touchdown was set up by a 64-yard catch and run by Kevin White, who barely stayed in-bounds as he ran down the left sideline to Arizona's three-yard line.