Rovers kicked off the new year with a five-star performance to move back into the play-off positions.
A frantic first-half saw Rovers take the lead with little over 40 seconds played, scoring the first goal of 2019 in Sky Bet League One, and that set the tone for the afternoon as the home side cruised to victory.
Rovers opened bright as Mallik Wilks - fresh from agreeing to extend his loan spell - received the ball on the right-hand side and floated in a brilliantly-weighted cross into the area, towards Alfie May who was all alone at the back post.
He was as equally impressive with his finish as the cross from Wilks, with his cushioned header looped into the net in the opposite corner.
Wilks would be at it again just 90 seconds later with another cross from the right this time finding John Marquis six yards out from goal, only for the striker to see his header saved superbly by Magnus Norman.
Norman would be a busy man in the Dale goal, with the stopper having to be alert to ambitious attempts from both the goal-scorer May and Ben Whiteman.
Wilks would have a chance of his own as he once again got the better of his man down the right, with the forward getting past Kgosi Ntlhe before shooting for the near post, looking to catch Norman out, but the Dale goalkeeper was alert to the danger.
Norman was not able to get anywhere near Rovers' next real attempt on goal, with Ali Crawford keeping up his own personal goal of the season competition with another stunner.
He stepped to curl a free-kick into the far corner from the tightest of angles to double Rovers' lead with the first half just reaching the half-way point.
Both Crawford and Andy Butler next came close to extending the lead further, with Crawford seeing Norman at full stretch to deny him from another free-kick, before Butler flashed a header wide from the resulting corner.
The third goal would arrive from another set-piece routine on 34 minutes, with Andrew playing a short free-kick to Marquis who in-turn laid the ball off to Whiteman.
He crossed into the area from the left-hand side of the box and there was Marquis to power home a header into the corner and give Rovers a three-goal lead at the interval.
After the break, the intensity died off, with the first real opportunity of the second period coming on 73 minutes as Crawford looked to catch Norman off his line with a neatly chipped effort, but he was unable to keep the ball below the bar.
Rovers did get a fourth goal, albeit via a huge helping hand from Dale stopper Norman with 15 minutes left to play.
Marquis took aim from distance with what was a tame effort in truth, but Norman palmed the ball into the back of the net as Rovers cruised towards three points.
There would be time for a fifth too, with Marquis playing the ball out wide to Matty Blair, who in-turn crossed the ball into the area for the on-rushing substitute James Coppinger, who duly obliged with a diving header into the corner.