The Chargers trailed 31-20 before Darryl Gamble recovered a Richard Bartel fumble in the Cardinals' end zone midway through the fourth quarter.
With 3:11 remaining, Volek led San Diego on a 12-play, 90-yard drive to account for the winning score. In all, Volek completed 9-of-17 passes for 123 yards.
Rivers' counterpart, Arizona quarterback Kevin Kolb, was equally effective. Following early field goals from Jay Feely and Nate Kaeding, the former Philadelphia Eagle gave the Cardinals a 10-3 lead when he connected with Larry Fitzgerald for an 80-yard touchdown pass.
Fitzgerald finished with three catches for 108 yards.
Patrick Peterson intercepted a Rivers' pass and returned it 34 yards for a score to give the Cardinals a 17-3 advantage after one quarter.
Kaeding booted a 36-yard field goal in the third quarter.