Feeley's 44-yarder in the third quarter drew the Cardinals even at 13-13 and his 29-yard kick early in the fourth put Arizona (3-2) ahead for good.
The Cardinals' defense also scored a pair of touchdowns provided by Kerry Rhodes and Dominique Rodgers-Cromartie.
The Saints (3-2) got 294 yards and two passing touchdowns from Drew Brees, but it wasn't enough to prevent their second loss in three games.
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