Jordan Rhodes hit a hat-trick as Rovers earned their first win under Henning Berg.
After Mauro Formica had opened the scoring after just three minutes, Rovers' record signing grabbed two quick-fire goals in the first half before adding a nodded goal in the second to make it a comfortable afternoon.
Markus Olsson and Martin Olsson both saw efforts hit the wood work whilst Morten Gamst Pedersen saw a goal chalked off late on.
For the home side they had Lee Tomlin's 88th minute strike as consolation.
The win sees Rovers pick up their second away win of the season, the three points moving the club back into the top six.
Henning Berg kept faith with the same eleven that started last time out in the draw with Birmingham City.
Gael Givet and Colin Kazim-Richards were back after injury but had to settle for a place on the bench.
Despite their lowly position it was the home side who started brightly, threatening in the opening two minutes with a series of corner kicks.
However Rovers held firm and took the lead with their first attack of the game after just three minutes.
It started with Adam Henley's run down the right flank. The youngster powering forward before crossing into the box, Mauro Formica let the ball run past him to Jordan Rhodes, the striker's shot was blocked, the rebound found Formica and he fired home for his first goal of the season.
Rovers continued with the forward play with another attack from Henley but this time Bobby Olejnik in the Peterborough goal denied Formica.
Ruben Rochina was the next player to test the Austrian 'keeper with a curling effort that was tipped wide, whilst at the other end Adam Henley was in the right place to clear inside his six-yard box from Craig Alcock's centre.
But that Peterborough attack only delayed the inevitable as a second goal for Rovers arrived on 20 minutes. Ruben Rochina spreading the ball wide for Martin Olsson and his centre was powered home by Jordan Rhodes.
Lee Tomlin was denied by a Scott Dann block on 28 minutes as the home side looked to find some way back in the game, Posh captain Michael Bostwick not too far off with a dipping drive that flashed over Paul Robinson's crossbar.
However six minutes from the break it was a third for Rovers and a second of the game for Rhodes. Grant Hanley starting the move with a timely interception, Danny Murphy set Ruben Rochina away and he curled a lovely ball behind the Peterborough back line for Rhodes to run onto and finish emphatically.
There was still time for Ruben Rochina to look for another goal but after his twisting run he fired narrowly over.
To their credit the home side started the second half lively with two chances inside the opening seven minutes.
A wayward pass from Danny Murphy went into the path of Danny Swanson, he teed up Saido Berahino for a shot that Robinson had to palm over the bar. Then a shot from distance from Grant McCann was a whisker wide.
On the hour mark Jordan Rhodes came close to grabbing his third of the game, Mauro Formica with a lovely forward ball, the striker rounds Olejnik but as he takes the ball wide he can only fire a yard past the far post.
On 78 Rovers were a whisker away from making it 4-0 when a ball from Rochina found Jordan Rhodes, his shot was deflected away from goal as far as Markus Olsson who arrived at pace to hit the ball goalwards only to see if bounce off the woodwork.
The goal would arrive from the resulting corner and it would be a first hat-trick in Rovers colours for Jordan Rhodes.
Mauro Formica delivered the ball from the right and as Scott Dann headed back across goal it left Rhodes with the simplest of chances, the Scottish international making it five goals in a week with a simple header.
With four minutes to go Rovers thought they had grabbed a fifth when after Martin Olsson's shot deflected against the woodwork substitute Morten Gamst Pedersen followed it in to score but the linesman on the right raised his flag much to the Norwegian's consternation.
Slack play from Ruben Rochina then presented Peterborough with a consolation goal on 88 minutes, Lee Tomlin making no mistake with a shot from distance to make it 4-1 to Rovers.
Rovers continued to look for further goals but were denied at the death by a fine double save from Bobby Olejnik denied Rochina and then Nuno Gomes.
It was an impressive display from Rovers, a first win for Henning Berg and a second away win of the season that moves us up to sixth.
PETERBOROUGH: Olejnik, Alcock (sub Anderson 77 mins), Brisley, Bostwick (c), Swanson (sub Ferdinand 64 mins), Tomlin, Boyd, McCann, Newell, Knight-Percival, Berahino.
Subs not used: Day (GK), Zakuani, Sinclair, Clarke-Harris, Gordon.
Goals: Tomlin 88 mins.
ROVERS: Robinson, Henley, Dann, Hanley, Martin Olsson, Formica, Etuhu, Murphy (c) (sub Lowe 60 mins), Markus Olsson (sub Pedersen 81 mins), Rochina, Rhodes (sub Nuno Gomes 82 mins).
Subs: Kean (GK), Givet, Vukcevic, Kazim-Richards.
Goals: Formica 3 mins, Rhodes 20, 39, 79 mins.