Goals from Connor Wickham and Josh Carson booked Town a place in the Fourth Round of the Youth Cup.
Town went ahead midway through the first-half when Wickham beat Tranmere 'keeper Joe Collister and Carson added to the scoreline just after the break following a well worked corner.
Town boss Roy Keane and his coaching staff made the long journey to Prenton Park to watch the game and saw Blues start the stronger with a good effort from Carson well saved by Collister.
Rovers began to get in the game and Conor Roberts shot just wide after a corner move involving Max Power, then Dale Jennings blasted narrowly wide of the right hand post after a good run.
At the other end David Cawley's corner was met by Tom Eastman but his header failed to find the target.
Wickham set up Caolan Lavery who couldn't get enough power on his header then it needed good work from Callum Bennett to clear off the Town line as Rovers threatened an opener.
Town got the breakthrough on 26 minutes, Billy Clark's tackle deflected the ball into Wickham's path who burst in on goal on the right side and curled his shot past Collister into the far corner.
Seb Dunbar was forced off for Blues with an injury just past the half hour, Rory McKeown his replacement, Cawley then booked for a strong challenge.
Blues doubled the lead on 54 minutes, Cawley played a short corner to Carson who cut inside and drilled the ball through a crowd of players into the bottom right hand corner.
Mirko Ranieri tipped Jack Mackreth's 25 yarder around the post as Rovers looked for a way back into the game but without any success as Town saw out the game without too many alarms.
Report: Blair Ferguson