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.
Administration delays decision on Keystone XL once more
Putin thinks Obama would save him if he were drowning