Will Grigg put the hosts ahead after just three minutes, but it was Ben Reeves who stole the show with two stunning goals.
The former Southampton trainee scored twice from 25 yards to hand boss Karl Robinson his first win over Posh since 2011.
The hosts were ahead inside four minutes after some clever work from Daniel Powell on the wing created space for a cross into Grigg, and the on-loan Brentford striker stroked home his 12th of the season from close range.
Posh went close to levelling after 20 minutes, but Erhun Oztumer’s long-range effort hit the crossbar.
Reeves doubled the Dons’ lead on the half-hour mark with a low, fizzing strike, which flew under the body of visiting goalkeeper Ben Alnwick.
Midfielder Reeves bagged his second before the break with another stunning effort as the Dons cruised to their second win in a row.