Rovers were left a man down after Junior Agogo was dismissed for kicking out at Phil Bolland in an off-the-ball skirmish.
Agogo's straight red from referee Gary Lewis came just after Richard Walker headed Rovers into a well merited two-goal lead and, from that moment, Paul Trollope's side never looked like losing their grip.
After winning four out of five under caretaker boss Steve Bleasdale, Posh were surprisingly defensive in the early stages against a Rovers side that had often seemed more relaxed on the road.
Posh were grateful for timely interceptions by Mark Arber and Jamie Day before Agogo missed a great opportunity when heading straight into Lee Harrison's hands.
But Agogo made no mistake on 36 minutes, riding the challenge of Chris Plummer before beating Harrison to boost hit tally for the season to 15 goals.
Ten minutes after the break Rovers outwitted Posh with a quickly taken free-kick. While home players were complaining about a booking for Adam Newton following a foul, Stuart Campbell simply swept the ball forward and Walker had time and space to pick his spot to head goal number 18 of the campaign.
Even after Agogo paid the penalty for his moment of madness, Posh could never really make their numerical advantage count and when substitutes Ryan Semple and Peter Kennedy did get well struck efforts on target, Rovers' goalkeeper Scott Shearer was in commanding form.
Skipper Dean Holden managed to pull one back for the home side in added time but the goal came too late for Posh to even have any thoughts of salvaging a point.