They had already carved out a host of opportunities when Gareth Evans broke the deadlock midway through the first half.
Michael Smith then opened his Blues account by converting a cross from the excellent Ben Davies just before the interval.
And Marc McNulty came off the bench to add a third in the second half for the rampant hosts.
The margin of victory could – and perhaps should – have been greater, but a combination of wasteful finishing and superb goalkeeping denied them even more goals.
And a fine free-kick from Lee Brown late on for the visitors proved nothing more than a consolation.
Paul Cook made three changes from the side beaten by Leyton Orient the previous week.
Evans replaced McNulty, as Pompey reverted to a more familiar 4-2-3-1 system, with Smith leading the line.
There were also a couple of switches in the defence, as Kieron Freeman and Matt Clarke made way for Davies and Adam Webster.
The first half was an entertaining, end-to-end affair, although it was the hosts who carved out the better chances.
Pirates keeper Steve Mildenhall made a stunning save in the opening seconds, somehow managing to claw away Christian Burgess’ header.
That came from a Davies corner and the right-back delivered another cross moments later that was nervously dealt with by the visitors’ defence.
The Blues certainly looked hungry and one flowing passing move involved Smith, Kyle Bennett and Gary Roberts, but the latter’s cut-back was intercepted.
Mildenhall was then Rovers’ saviour once more, this time doing well to deny Bennett at his near post.
But the keeper could do nothing to prevent Pompey from taking a deserved lead on 19 minutes.
Smith played a superb cross-field pass to Davies and his ball into the box was deftly flicked home by EVANS.
Rory Gaffney came close to levelling when he rattled the crossbar at the other end, although it would have been a controversial goal, as Roberts was lying injured on the turf.
Rovers had certainly grown into the game and it took a fine challenge by Webster to halt Daniel Leadbitter’s dangerous run.
It was still Pompey looking most dangerous, however, and Smith could not quite sneak a shot past Mildenhall after collecting Webster’s raking pass.
Evans and Roberts should both have done better late in the half, with the duo failing to find the target from close range.
But any feelings of frustration were lifted when the hosts did double their advantage in the third minute of stoppage-time.
It was Davies who provided the assist once again, collecting the loose ball after his corner had been blocked and picking out SMITH to head home his first Blues goal.
Bristol Rovers 0
Evans had an early attempt once the second half got underway and Mildenhall had to tip the ball over the bar.
He then tried a more acrobatic effort after connecting with Bennett’s cross, but this time it flew wide.
The visitors were looking nervous and Tom Lockyer had to hack clear after Mildenhall and Tom Parkes made a mess of dealing with Davies’ low cross on 50 minutes.
And Smith really should have added to his goalscoring account soon after, somehow sliding wide from a few yards out when Roberts’ pass found him unmarked in the box.
The same duo then combined again, but this time Mildenhall came tearing off his line to deny Smith.
Cook made his first change on 69 minutes and it was the tiring Smith who made way for McNulty up front.
Adam McGurk then came on for the impressive Roberts as the game began to drift towards a conclusion.
But it exploded back into life on 77 minutes when McNULTY latched onto Bennett’s threaded pass and slotted the ball into the bottom corner.
It almost got worse for the ailing Pirates, only for Mildenhall to once again make a stunning save to deny Evans from point-blank range.
McGurk almost got in act as well, but his curling effort was diverted over the bar by the head of Brown.
Instead it was Rovers who grabbed a late consolation when Brown hammered home a ferocious free-kick from the edge of the box.
But that failed to dampen the spirits of the Fratton faithful, who saw their side return to the top seven on a comfortable afternoon.
Pompey (4-2-3-1): Fulton; Davies, Burgess, Webster, Stevens; Close, Doyle (c); Evans, Roberts (McGurk 75), Bennett (Chaplin 86); Smith (McNulty 69)
Goals: Evans 19, Smith 45+3, McNulty 77
Subs not used: Bass, Clarke, Barton, Tollitt
Bristol Rovers (4-3-3): Mildenhall; Leadbitter, Lockyer, Parkes, Brown; Sinclair, Mansell (c) (Montano 55), Lawrence (Lines 77); Bodin, Gaffney, Easter (Taylor 55)
Goals: Brown 90+1
Booked: Easter, Brown, Montano, Lockyer
Subs not used: Puddy, McChrystal, Clarke, Fallon
Referee: Trevor Kettle
Attendance: 17,808 (2,863 away fans)