Rovers roared into a comfortable 3-0 lead and although the home side hit back with two late goals, David Lowe's charges saw the game out to claim the win.
After a slow start at Carlisle's training ground it was Rovers who opened the scoring after a penalty decision.
Great forward play by Lewis Mansell was ended when the attacker was brought down in the area. Ramirez Howarth took the spot-kick and although his effort was saved, Stuart Callaway was on hand to follow-up and score.
The lead was extended shortly after half-time when good combination play between Ollie Mehew and Sam Joel saw Mehew grab his first Rovers goal with a smart finish.
Then on 64 minutes the forward returned the compliment by laying on the ball for Joel to find the back of the net, his third strike this pre-season.
As the half wore the home side started to take control of the game, pulling two goals back to ensure a tense finish. But Rovers held on to secure the victory.
"It was a tough task for us having played on Saturday and then Tuesday," said coach David Lowe.
"It was a decent result for us, we played good football for an hour, although towards the end we lost control of the game both technically and tactically. But overall it was a pleasing performance."
The under 18s are back in action this Friday when they play Rangers at their training ground, kick-off 2.00pm.
ROVERS: Wilson (sub Williams 46 mins), Nyambe, Platt, Scott, Pirretas, Edo, Pierce (sub Hardcastle 46mins), Tomlinson (sub Callway 66 mins), Mansell (sub Mehew 46 mins), Howarth (sub Mansell 66 mins), Callaway (sub Joel 46 mins).