Rory Loy's first-half strike ensured Carlisle inflicted a second defeat in three games on League One leaders Tranmere.
Rovers were reduced to 10 men when Jean-Louis Akpa Akpro was sent off for kicking out at Frank Simek.
Carlisle took the lead when Loy connected with Matt Robson's cross and his bobbling shot found the net.
Liam Palmer had the ball in the net for Tranmere but his close-range finish was ruled out for offside.