Goals in each half from Danny Murphy and Grant Hanley saw Rovers gain safe passage through to the fourth round of the FA Cup with Budweiser.
In a dominant display from a strong home side, Danny Murphy's 25-yard strike after just 7 minutes set the tone with the visitors offering little in response.
Chances came and went before Rovers doubled their lead on 58 minutes. A half-cleared corner kick was put back into the area and Scott Dann squared for Grant Hanley to fire home from close-range for his third of the campaign.
Like the first half, Rovers had chances to add further goals, but whilst they didn't come, it was a satisfactory afternoon as they made it three wins in succession to put Rovers in the hat for Sunday's draw.
Ahead of the game, interim boss Gary Bowyer resisted the urge to make wholesale changes to his squad for the cup visit of Bristol City, making just the one alteration to the eleven that did so well against Nottingham Forest in the league last time out.
The only change saw Diogo Rosado back in the starting line-up with Joshua King, who signed permanently for the club on Wednesday, dropping to the substitute's bench.
Rovers had named an attacking line-up once more but it was from one of their more defensively-minded players that they grabbed the opening goal.
It came on seven minutes when Danny Murphy intercepted a pass inside by Bristol right-back Mark Wilson, the Rovers captain taking full advantage to race goalwards, and although he had options left and right that Murphy could have passed the Rovers captain had other ideas and blasted the ball into the top corner of the goal from 25 yards.
The visitors looked to get back quickly when a cross from the right was nodded back into the path of former Rover Jon Stead but his header was well over the bar. It would prove to be one of just two efforts at goal for the visitors.
A lovely turn and shot from Colin Kazim-Richards saw Tom Heaton in the City goal dive full length to tip it around the post, before the Rovers striker skimmed the roof of the net after neat play by Ruben Rochina.
Rovers continued to be neat and tidy in possession, pinning their opponents back for long spells, Kazim-Richards denied by a block from Liam Fontaine before his centre just evaded the outstretched boot of Diogo Rosado.
As comfortable as Rovers were, they were dealt a blow on 34 minutes when Adam Henley pulled up with what looked like a hamstring injury, the young full back unable to continue. Simon Vukcevic on as his replacement in a reshuffle that saw Jason Lowe move to right back.
Rovers continued to pose the greater threat but on the stroke of half time the Robins went close once more, Ryan Taylor forcing Jake Kean into tipping over his own bar with a well-placed header.
The second half was slower to get going but Rovers were never in any trouble from the visitors, the only question would be when the second goal would arrive and that was answered just before the hour mark.
Initially a Morten Gamst Pedersen corner from the left just evaded the head of Grant Hanley, but as the ball came out Ruben Rochina delivered over to Scott Dann who chested down before finding his defensive partner Hanley who forced the ball home.
Rovers continued to dominate with a host of chances created. Makeshift right-back Simon Vukcevic seeing an effort saved by Heaton.
The threat then came down the opposition flank with Martin Olsson twice going close, the Swedish international fired just wide of the post with his right-foot before forcing Heaton with a shot across the bows moments later.
For the visitors, they rarely threatened. Steven Davies shot straight at Jake Kean, whilst substitute Martyn Woolford was wasteful with a volley at the back post.
For all their possession and attacking play Rovers really should have had more goals to show for their dominance, Kazim-Richards and Ruben Rochina both going close in the latter stages.
A third goal didn't arrive but it was a comfortable day for Gary Bowyer's side as they booked their place in the fourth round draw with ease to make it a fine week with three wins.
ROVERS: Kean, Henley (sub Vukcevic 35 mins), Dann, Hanley, Martin Olsson, Lowe (sub Pedersen 63 mins), Murphy (c), Rosado (sub King 77 mins), Rochina, Kazim-Richards, Rhodes.
Subs not used: Sandomierski (GK), Nuno Gomes, Goodwillie, Fernandez.
Goals: Murphy 7 mins, Hanley 58 mins.
Booked: Rosado, Hanley.
BRISTOL CITY: Heaton, M. Wilson (sub Reid 63 mins), Fontaine, Carey, Stead (sub Davies 60 mins), J. Wilson, Skuse (c), Pearson, Cunningham (sub Woolford 70 mins), Taylor, Anderson.
Subs not used: Gerken (GK), Edwards, Burns, Bates.