A sparkling brace by Tom Lawrence was added to by goals from David Amoo and James Berrett before Ryan Lowe grabbed a late consolation header for Tranmere.
On-loan Manchester United teenager Lawrence, making his first league start, stunned Tranmere with a brilliant first-minute strike from 25 yards.
The Rovers defence failed to clear after Lee Miller had challenged for a header and Lawrence seized on the ball to send a dipping right-footed shot past goalkeeper Owain Fon Williams.
There was an open nature to the game, with Rovers' Kristoffer Peterson just denied after a great solo run before Fon Williams was at full stretch at the other end to claw away Prince Buaben's 20-yard blast and deal with a deceptive Matty Robson effort which almost crept in beneath the crossbar.
Lawrence impressed with his powerful shooting when Carlisle won a free-kick 35 yards out. Fon Williams was glad to parry a bullet of a shot which came through a crowd of players.
Peterson was again Tranmere's dangerman, coming within inches of equalising in the 38th minute when he found space on the left to slide the ball tantalisingly across the face of the Carlisle goal.
Amoo made it 2-0 in the 52nd minute, lashing home Berrett's right-wing corner on the volley from eight yards out. It was the former Tranmere forward's eighth goal of the season.
Miller nearly added to Carlisle's tally when he slid a low shot against the post, but there was no holding the home side and Lawrence produced a goal of the season candidate in the 67th minute with a mazy dribble through the heart of the Rovers' defence before firing left-footed past a stranded Fon Williams.
Amoo's dash down the left flank set up Carlisle's fourth, a fierce right-footed drive from just inside the area by Berrett.
Ryan Lowe pulled a goal back in the 81st minute with a far post header from Peterson's cross, but it was too little too late for Tranmere.