Favre threw for a career-high 446 yards with two touchdowns and two interceptions for the Vikings (3-5), who fought back cheers of "Fire Childress!" -- referring to embattled Minnesota coach Brad Childress -- early in the game to pull out the win.
The Cardinals (3-5) led 24-10 with 4:39 to play, thanks to a 96-yard kick return by LaRod Stephens-Howling and a 30-yard fumble return by Michael Adams on another kickoff.
But Favre directed scoring drives of 40 and 77 yards in regulation, and Adrian Peterson's 30-yard run in overtime keyed the winning drive.