Rovers were full value for their two-goal victory and it could have been a lot more as they were denied by the woodwork on three occasions.
The visitors went ahead in the 12th minute with an excellent angled shot by Andy Williams after he had been set up by Rickie Lambert.
David Pipe volleyed against a post from 20 yards five minutes later and ahead of the break Lambert struck the outside of a post from the corner of the box.
Steve Jennings volleyed over early on for Tranmere and it was not until the 55th minute that Rovers keeper Steve Phillips was tested when he made a diving save from a Gareth Taylor header.
Bristol Rovers doubled their lead in the 58th minute with a good finish by Lambert after the ball bobbed around in the box following a long throw-in.
Tranmere sent on strikers Craig Curran and Calvin Zola to try to salvage something from the game, but a Zola header was held by Phillips and the keeper made another fine save from the same player in the 73rd minute.
Substitute Craig Disley became the third Rovers player to hit the woodwork in the 82nd minute.
Tranmere could make few inroads as the visitors defended stubbornly and it summed up their night when Andy Taylor volleyed off target in injury time.
Williams, Lambert and skipper Stuart Campbell were excellent for the winners, while few emerged with any credit in a woeful Tranmere display which left manager Ronnie Moore totally frustrated.