First-half goals from Chris Wood and Elliott Bennett put the Seagulls in charge of Saturday’s League One clash at the Withdean Stadium, and Wood struck again to make it three 10 minutes after the break.
But Lee Tomlin headed in a cross by Craig Mackail-Smith after 66 minutes and Posh were foiled when Chris Whelpdale and Grant McCann both fired against the crossbar in the closing stages.
Peterborough had skipper McCann sent off deep in stoppage time after he received a second yellow card.
Wood, on loan from West Brom, had a goalbound shot cleared off the line before he gave Brighton the lead at the near post after 25 minutes following a fine low cross by Bennett.
Former Wolves winger Bennett doubled the advantage only two minutes later with a stunning shot from 18 yards as the Peterborough defence backed off. Wood pounced to hit his second goal 10 minutes after the interval by forcing in a low cross by Glenn Murray.