After going behind early on to a Rickie Lambert header, they made their superior organisation work for them.
With Simon Hackney pulling all the strings from midfield, Rovers had little hope of coming back once their lead had gone, but they never stopped trying and substitute Andy Williams pulled back a goal in injury time.
There were three goals in the first half all from set-pieces. Carlisle helped Rovers to the first after failing to deal with a free-kick conceded by their captain Paul Thirlwell around the box.
From the right of goal, Craig Disley picked out Lambert and the striker's header accurately placed the ball wide of Ben Williams, who was making his debut in Carlisle's goal.
The lead lasted barely three minutes as the visitors swept up-field to win three corners in a row.
Rovers keeper Steve Phillips fisted the first two over the bar so Hackney played the third one short to Marc Bridge-Wilkinson.
His ball in was too much for the defenders who barely moved as Danny Carlton's confident header found the net.
Another Hackney corner, this one from the left, saw his side go ahead in time added to the first half.
The flag-kick was headed out but only as far Bridge-Wilkinson on the edge of the area and fired back in an accurate left-foot drive.
Rovers could hardly complain as, between the goals, Hackney had beaten Phillips with a shot which bounded off the base of the keeper's right post.
Carlton scored again ten minutes from time to put the game beyond Rovers, but they finished strongly with Williams, who had replaced Chris Lines, hitting the consolation after a rare mistake in the Carlisle defence.