The win was their second in the row after the victory over Hull City in the previous match – the first time they have managed to do so this season.
Harrison Burrows initially equalised for Peterborough United on the hour mark, before Siriki Dembele caused the stadium to erupt with an injury-time winner.
The victory means Posh remain in 20th place in the Championship, however they extend the gap between themselves and the relegation zone to five points.
Darren Ferguson’s side will travel to Wales next weekend to take on Swansea City and former Posh defender Russell Martin.
The Swans currently sit in 16th – three points ahead.
Here are the best of today’s Championship rumours...
9. Nottingham Forest linked with move for Sheffield United striker
Nottingham Forest are reportedly keen on signing Rhian Brewster during the January window, with Steve Cooper keen to reunite with the forward. Brewster enjoyed a brilliant spell with loan Swansea City - scoring 11 goals in 22 appearances. (Sunday Mirror) Photo: Laurence Griffiths