A deadly second half display ensured Rovers grabbed another victory on the road and with it, made it a fantastic five league wins in a row.
After going a goal down thanks to Steven Taylor's header, Rovers battled back with a stunning trio of goals in 13 second half minutes to gain control, with strikes coming from Charlie Mulgrew and a Bradley Dack brace.
Jack Marriott's late tap in was just a consolation as Rovers sent the 1,000+ supporters back to Lancashire in buoyant mood.
Craig Conway started for the first time since October after recovering from a hamstring injury, as Tony Mowbray's men went in search of a fifth straight league win.
Conway was one of two changes from the last league game at Blackpool, with Dominic Samuel rewarded for his recent goalscoring form by starting in place of Danny Graham.
Midfield pair Rekeem Harper and Elliott Bennett missed out through suspension, and there was a place on the bench for youngster Willem Tomlinson.
Rovers came flying out of the blocks and could have taken the lead inside the opening four minutes but after latching onto a Richie Smallwood cross, Samuel could only head over the upright from close range.
At the other end, Marriott fired over the bar from the edge of the box in a lively opening at a chilly ABAX Stadium.
A lovely move from Rovers ended with Samuel teeing up Dack who volleyed wide before the same players combined again and forced goalkeeper Jonathan Bond into a smart stop to deny Dack once more.
However, Rovers were undone by a set piece just a minute later as Marcus Maddison's inswinging corner was powerfully headed home by former Newcastle defender Taylor at the back post.
Rovers' were under pressure as the host looked to increase their advantage and Marriott again was given space to go for goal but once more fired over Raya's upright.
Rovers were force into a change just after the half hour mark with Peter Whittingham forced off with a calf injury and Corry Evans entered the action in replacing the experienced ex-Cardiff man.
With ten minutes to go until the break, Marcus Antonsson wriggled past his man but saw Bond tip his near post drive past the post as Rovers searched for a route back into the clash.
At the other end, the dangerous Gwion Edwards cut in before smashing just wide of the target as Posh continued to ask questions of the Rovers' backline.
A replacement was replaced at half time as Evans couldn't shake off an ankle injury after being clattered into just before the half ending and Tomlinson came on to replace the Northern Ireland international for the start of the second half.
Whatever Mowbray told his players at half time paid divedends as that man Charlie Mulgrew was lurking at the back post to tap home after Paul Downing flicked on Dack's wicked corner.
And a good response turned into a great one as Rovers took the lead through Dack.
The midfielder played an excellent one-two with Smallwood before picking his spot and calmly finding the bottom corner with a ruthless finish just four minutes later to turn the game on its head.
And a devastating counter attack saw Rovers add a third to their tally. Samuel found Antonsson flying up the left, who in turn passed to Dack, who confidently beat Bond again to completely give Rovers control of the game.
Rovers were smelling blood against a shell-shocked Posh and Antonsson came so close to getting on the scoresheet but saw Bond bat away his curling effort.
The visitors had a flurry of bodies on the line to deny Peterborough from finding a way back into with 15 minutes remaining.
Any chance Peterborough would have had to get back into the game looked to have been extinguished with just four minutes remaining as substitute Danny Lloyd headed over the bar after Edwards picked him out, before Raya did excellently to deny Marriott a moment later.
But Marriott wasn't to be denied and in added time he scored his 13th of the season from close range after Lloyd's low cross from the left.
There was still time for Peterborough to go down to 10 men when captain Jack Baldwin was shown a second yellow for a cynical challenge on Dack in the dying embers of the encounter.
And that was to be the last action of the game as Rovers continued their charge up the table and moved into third in League One.
PETERBOROUGH: Bond, Hughes, Tafazolli, Baldwin (c), Edwards, Forrester (Doughty, 70), Maddison, Marriott, Anderson (Lloyd, 66), Taylor, Grant (Kanu, 85).
Unused substitutes: O'Malley, Miller, Penny, Freestone.
Goals: Taylor, 11, Marriott, 90.
Booked: Baldwin, 3, 90.
Sent off: Baldwin.
ROVERS: Raya, Nyambe, Downing, Mulgrew (c), Williams, Smallwood, Whittingham (Evans, 32) (Tomlinson, 46), Conway, Antonsson, Dack, Samuel (Graham, 76).
Unused substitutes: Leutwiler, Ward, Caddis, Nuttall.
Goals: Mulgrew, 48, Dack, 52, 58.
Booked: Antonsson, 30, Smallwood, 61.
Attendance: 6,164 (1,068 away).