Dutchman Yanic Wildschut rode a series of tackles to put the Latics ahead and played his part as Will Grigg doubled their lead shortly after.
Posh halved the deficit when Erhun Oztumer pounced before substitute Souleymane Coulibaly equalised.
However Power raced onto Grant Holt's pass to find the winner and put Wigan a point outside the League One play-offs.
Max Power's late strike gave Wigan all three points after Peterborough has fought back from two goals down.