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...
5. American businessman confirms interest in buying Derby County
American businessman Chris Kirchner has confirmed his interest in Derby County and has formally applied to the club's administrators. Kirchner is co-founder, chief executive and chairman of software company Slync.io, a global logistics technology provider. (Derby Telegraph) Photo: Ashley Allen
6. Celtic monitoring Derby County full-back
Celtic have been linked with a possible move for Derby County defender Lee Buchanan. The Scottish club were reportedly interested in signing the 20-year-old over the summer, with Nottingham Forest also keeping tabs on him. (Glasgow Times) Photo: Laurence Griffiths
7. Tottenham Hotspur keeping tabs on Championship keeper
Tottenham Hotspur are reportedly monitoring the situation of West Brom goalkeeper Sam Johnstone, who is tipped to leave the Hawthorns. Nuno's side only signed second-choice shotstopper Pierluigi Gollini from Atalanta in the summer. (Birmingham Live) Photo: Pool
8. Peterborough United leading race to sign Man City target
Peterborough United and Nottingham Forest are leading the race to sign Hornchurch's young prospect Jili Buyabu. The 19-year-old was handed a trial by Chelsea over the summer and Manchester City, Middlesbrough and Bournemouth are also keeping tabs on him. (Non-League Paper) Photo: Alex Pantling