Substitute Stephen Dobbie scored a stoppage-time winner to end Brighton's seven-game winless streak.
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Posh looked to be heading for the first draw of the season on the back of a resolute defensive performance which had frustrated the Seagulls for most of the evening.
However, Dobbie came off the bench to sneak a goal two minutes into stoppage time, giving Gus Poyet's men their fifth successive win over the London Road outfit.
The Seagulls, particularly Craig Mackail-Smith, were wasteful on a number of occasions. Andrew Crofts fired over in the first period while Mackail-Smith, normally so assured in front of goal, squandered two headers.
Brighton were by far the better side in the second half but found goalkeeper Robert Olejnik in inspired form when they could find the target, and they had a post to thank as Andrea Orlandi drilled an effort against the woodwork.
However, Brighton's frequent forays forward were eventually rewarded at the death as Dobbie registered his first-ever goal for the club by lifting the ball past Olejnik.
Both sides' recent poor form was evident in the opening exchanges as they proceeded with trepidation which led to a lack of chances.
It was Brighton who eventually threatened one of the goalkeepers, though, when the tricky Will Buckley created an opening for Crofts, only for the ex-Norwich midfielder to fire over.
The prolific Mackail-Smith ended a four-game spell without a goal when he found the net twice in a draw with Leeds last Friday, but he was unable to make the most of the opportunities which fell his way here.
First, the Scottish international, who would have had a hat-trick against the Whites had he not missed a penalty, headed tamely at Olejnik.
Mackail-Smith then met another flighted cross with his head but could only flick the ball wide as a forgettable first 45 minutes drew to a close.
Poyet's half-time words clearly had their desired effect on the Seagulls as they upped the ante after the interval.
Ashley Barnes' driven shot from distance forced Olejnik to push the ball around a post as the home crowd stirred into life.
Buckley looked the most likely to make something happen and Olejnik was tested once more as the winger's venomous effort swerved in front of him, with Buckley heading the subsequent rebound well wide.
Poyet's side came closer still just before the hour mark as Orlandi let the ball run across his body before firing a left-footed effort against a post.
And the home supporters must have thought the deadlock would finally be broken when the ball dropped to Mackail-Smith 12 yards out shortly afterwards. However, the prolific frontman skewed a chance well wide to audible groans.
Substitute Dobbie had a goalbound-effort blocked before Poyet handed Will Hoskins his first league appearance of the season in place of the ineffective Mackail-Smith.
And the replacements paid dividends right at the end as Barnes slipped the ball through for Dobbie, who kept his composure to fire home and end the Seagull's long wait for a league victory.