Rovers made the brighter start. Charlie Barnett brought a good near-post save from Ben Williams, before Chris Shuker was off-target with a speculative long-range effort when he spotted the keeper off his line. Then Williams held a Steve Jennings effort at the second attempt.
United gradually warmed to their task. Scott Dobie headed wide from a corner and then home keeper Danny Coyne made a fine blocking save from Danny Graham after a defensive error. Coyne then did well to deny Graham again at the expense of a fruitless corner.
It was lively end to end fare. Ian Moore tested Williams with a well struck overhead shot midway through the half and soon after Ed Sonko found the sidenetting from 12 yards. There was a let-off for Rovers on 34 minutes when Graham hit a post. Soon afterwards Coyne turned a Cleveland Taylor cross against the bar.
As play swung the other end Shuker put an angled shot just wide. Home skipper Antony Kay did not appear for the second half with Gareth Edds taking over. But Rovers took the lead on 49 minutes with Moore netting in a scramble following a part cleared corner.
They doubled the lead on 53 minutes. Edds netted off the underside of the bar from Sonko's pass after a fine attacking move. Carlisle hit back on the hour as Graham deceived Coyne with what appeared to be a mis-hit shot from a Paul Thirlwell centre.
But the two-goal advantage was restored when Jennings blasted home on 66 minutes following an Andy Taylor throw-in. Moore made it 4-1 with a superb strike on 77 minutes after good work by Sonko to complete a disastrous second half for the visitors.