Goals from Aaron Cresswell, a first of his league career, and Ian Moore assured a 14th home success.
The home side had the better of the opening stages but Gareth Edds headed wide from a corner before Cresswell was off-target with a 30-yard strike.
Cresswell then saw a 25-yard free-kick saved comfortably by Steve Phillips.
Darryl Duffy completely mis-hit his shot when given a good opening for Bristol Rovers from a long clearance on 17 minutes.
The home side continued to make much of the running but Bas Savage had no luck with an angled strike.
But the Merseysiders took the lead on 37 minutes. A Cresswell free-kick from the corner of the box conceded by Steve Elliott appeared to take a deflection that pushed it out of the reach of Phillips.
As Rovers rallied, a David Pipe effort was deflected over the bar by home midfielder Antony Kay with Ricky Lambert heading over from the subsequent corner.
Phillips palmed away a dangerous Savage shot soon after the break while at the other end Danny Coyne made a comfortable stop from Duffy.
Bristol Rovers sent on Craig Disley and Jo Kuffour just short of the hour but moments later Savage missed a great chance to double the home side's lead when firing wide.
Disley was the second player cautioned on 62 minutes for diving and Bristol Rovers fell two behind two minutes later. A great run by Cresswell set up Ian Moore who finished well past Phillips.
Ed Sonko went close to a third on 64 minutes with his effort shaving the bar.
Savage for kicking the ball away and Ian Goodison collected second-half bookings for Tranmere.
Cresswell was excellent for the winners. Byron Anthony and Ryan Green tried hard for Bristol Rovers, but little went right for them.
Later on Lambert saw a free-kick saved by the outstretched leg of Coyne before the keeper held the subsequent header by Duffy.