Although the Dons finished with ten men after Drissa Diallo was sent off, inspired by skipper Keith Andrews they resisted strong late Posh pressure to claim all three points.
The visitors made the early running keeping the ball on the ground and forcing the Dons to concede a succession of free-kicks, one of which was touched to Charlie Lee who strode forward and rattled the crossbar with a 25-yard shot.
Dean Lewington charged down Josh Low's pass but wasted the Dons' first opening, shooting well wide. The league leaders fared little better on the opposite flank with Mark Wright's cross headed away by Shane Blackett.
The visitors' first effort on target came on 33 minutes with Colin Cameron cutting inside at the end of a patient build-up only to see his rising shot from just outside the area well held by Posh's Mark Tyler.
The home side made progress towards the end of the half but, after George Boyd should have done better with a headed chance, the former Stevenage man forced Willy Gueret into a diving save and the Dons goalkeeper also reacted well to deny Low in stoppage time.
The Posh failed to retain the initiative after the break and were stung by two goals in the space of ten minutes.
Kevin Gallen broke the deadlock just two minutes after the restart, sweeping an Andrews pass beyond Tyler's reach and it was skipper Andrews who fired the second from the tightest of angles running in from the right on 57 minutes.
Aaron McLean gave Posh hope, forcing the ball into the net on 75 minutes as Lee's drive dropped after hitting the bar and, two minutes later, the Dons were reduced to ten men when Diallo was red carded after a second bookable offence.
However, Paul Ince's side hung on to the three points to improve their position at the top of the table.