Neither goalkeeper was really tested in the first half. Terry Gornell was off target for Tranmere and Craig Curran volleyed over the crossbar.
Carlisle's Adam Clayton saw an early shot claimed by Luke Daniels and volleyed wide eight minutes ahead of the break.
Rovers began the second half well and Ash Taylor flashed a header wide from a Paul McLaren free-kick.
Tranmere should have taken the lead after 64 minutes but Ian Thomas-Moore missed the target with a simple chance after Curran's effort came back of the crossbar and that was as close as either side came to breaking the deadlock.