Peterson's score with 7:15 remaining capped a 14-point, fourth-quarter rally for the Cardinals. They had tied the score 3 1/2 minutes earlier when Kevin Kolb found Early Doucet over the middle for a 70-yard scoring strike.
Kolb finished 18-of-27 for 309 yards, two touchdowns and no interceptions, while Doucet made three grabs for 105 yards for the Cardinals (1-0).
Heisman Trophy winner Cam Newton made his NFL debut a memorable one for the Panthers (0-1), completing 24-of-37 passes for 422 yards, two touchdowns and one interception.
Newton connected with Steve Smith on scoring tosses of 77 and 26 yards and ran the ball eight times for 18 yards.