Neil Roberts and Steve Foster did the damage in a result that adds to the mounting problems of Barry Fry's relegation-threatened side.
Posh, with teenagers Ryan Semple and Ahmed Deen pitched into the battle and fellow youngster Jamie Day brought on as a substitute, started well only for Steve Thomson to fire wide when Calum Willock's third minute header rebounded off the Rovers' bar.
Thomson also failed to hit the target from close range following Semple's strong cross, although Greg Blundell's finishing was equally wayward when he was presented with Rovers' first clear-cut chance.
Posh's Mark Tyler was the busier keeper dealing well with the succession of corners as Rovers finished the half as the stronger side.
It was a momentum they maintained after the break and Tyler was forced to save at full stretch from Roberts.
The Doncaster man went one better on 55 minutes, calmly turning the ball into the net at the far post when Blundell's cross eluded Tyler and defender Sean St Ledger's desperate attempt to clear.
Posh fought hard for an equaliser but to Fry's despair they failed badly in front of goal.
Wayne Purser, sent clear by another Semple break, shot into the side netting and later, when un-selfishly set-up by substitute Richard Logan, failed to get the bell past Andy Warrington.
It was left to Rovers skipper Foster to make the points safe with nine minutes left when he took advantage of none-existent marking to steer in a header following a corner.