Peterson carried the ball a career-high 34 times and finished the season with an NFL-best 2,097 yards -- just 9 yards shy of Eric Dickerson's all-time, single-season record.
His run of 26 yards to the Green Bay 11-yard line with 3 seconds remaining set up a game-winning field goal by Blair Walsh, which hoisted Minnesota (10-6) into the NFC's sixth and final post-season seed.
The Vikings' fourth straight victory, coupled with the Packers' loss, set up a rematch between the two teams in next week's wild card round.
Christian Ponder fired three touchdown passes en route to 234 yards on 16-of-28 efficiency as the Vikings completed a remarkable turnaround following their 3-13 performance of 2011.
The Packers (11-5) fell despite Aaron Rodgers' four-touchdown game, in which he threw for 365 yards on 28-of-40 passing.
Greg Jennings led Green Bay's receiving corps with eight grabs for 120 yards and two scores.