Debutant Craig Davies gave Brighton the lead, but Craig Mackail-Smith and Aaron Mclean replied for Posh before Jim McNulty equalised on the stroke of half-time.
Adam Virgo tripped George Boyd to allow Dean Keates to make it 3-2 from the penalty spot and Mclean followed in a goal bound shot from Mackail-Smith to wrap up victory 14 minutes from time.
Davies broke the deadlock from close in after Posh keeper Joe Lewis failed to hold a low shot from French winger Seb Carole and the former Oldham striker had the simplest of tasks to turn the ball into an unguarded net.
Posh hit back to equalise when Mackail-Smith ghosted in to powerfully head home an in swinging cross by Paul Coutts. Mclean pounced to put Peterborough ahead with his 12th goal of the season after Brighton keeper John Sullivan could only parry George Boyd's shot.
But Brighton levelled in first-half stoppage time through defender McNulty, who scored with a half-volley from six yards after Tommy Elphick flicked on a Carole corner.