Richard Logan's cool finish and Mark Arber's tap-in ensured Posh banished the memories of their heavy defeat to the Dons in the first round of the league cup back in August.
Nineteen-year-old rookie Luke McShane was thrown in for his Posh debut minutes before kick-off after regular keeper Mark Tyler picked up a back injury in the warm up.
And the young stopper was almost tested just five minutes in, when Ben Chorley struck the bar from the edge of the box after the Peterborough defence failed to properly clear Gary Smith's free-kick.
Posh hit back and after Gareth Edds had almost hooked the ball into his own net, Callum Willock's fierce low strike was well saved by David Martin in the Dons' goal.
From the resulting corner Arber got away from his marker Smith, but Paul Mitchell cleared his goalbound header off the line.
At the other end, Dean Lewington somehow headed over unmarked from just four yards after getting on the end of Smith's in-swinging free-kick.
But it was Posh who continued to dominate and Willock was once again foiled by Martin - in for the cup-tied Matt Baker - midway through the first half.
The Dons' young stopper acrobatically tipped the striker's glancing header wide of the post, and then watched Steven Thomson's dipping 25-yard strike fly inches over the angle from the resulting corner.
Allan Smart's curling 20-yard free-kick came close to breaking the deadlock for the home team against the run of play just before the interval, but it clipped the top of the bar with McShane struggling to reach it.
Peterborough deservedly broke the deadlock in first-half stoppage time when Logan got on the end of David Farrell's clever flick and finished well past Martin.
Willock came close to extending the lead seven minutes after the break, but his shot after a mazy run fizzed across the face of goal.
But the visitors were not to be denied and the influential Arber made it 2-0 with a simple tap-in 12 minutes after the interval.
The hapless Martin in the Dons' goal saved Arber's initial header from Andy Legg's dangerous free-kick, but the big centre-half was on hand to finish the rebound from just two yards.
Dons' boss Danny Wilson threw on veteran centre-half Steve Palmer as a makeshift striker in the closing stages in a bid to get his side back in the game.
But Milton Keynes hit the bar for the third time late on, through sub Jason Puncheon's 20-yard piledriver, capping off a miserable day.