Trailing 24-10 in the fourth quarter, Minnesota scored twice in the last 3:34 to tie the game.
Adrian Peterson (144 yards, two touchdowns) pulled Minnesota to within seven points with a 4-yard TD run. Then, with 27 seconds left in the contest, Brett Favre (446 yards with two interceptions and two touchdowns) hooked up with Visanthe Shiancoe on a 25-yard scoring strike to tie it.
Longwell's boot 5:18 into the overtime gained the win for Minnesota (3-5), who broke a two-game losing streak amid speculation head Coach Brad Childress would soon be fired.
Derek Anderson started for the Cardinals (3-5) and completed 15-of-26 passes for 179 yards with a touchdown.
Larry Fitzgerald rolled up 107 yards on seven receptions in the loss.