Kevin Gall and Karl Hawley looked to benefit from the new line-up, with Derek Holmes spearheading the frontline.
Man of the Match Hawley had a hand in Carlisle's first goal and grabbed the second himself to top off one of his best ever displays for the Blues.
He signalled his intent early on, Cheltenham keeper Shane Higgs fingertipping his 20-yard drive over the bar, after Higgs had been smartly off his line to collect Hawley's first-time ball into the box for Gall to chase.
Cheltenham, struggling to cope with Carlisle's pace, might have been in front against the run of play.
Peter Murphy kicked a 25-yard drive from Mickey Bell off the line with Keiren Westwood beaten and Chris Lumsdon saved Westwood's blushes when he cleared Jamie Victory's header off the home line on the quarter hour.
Holmes and Hawley linked before Hawley sent Simon Hackney down the wing to set up Carlisle's 27th minute opener.
Gavin Caines appealed vainly for offside as Hackney left him in his wake and crossed for the unmarked Gall to steal in for a far-post header.
Then Holmes stole the ball from Victory to set up Carlisle's second.
He held on until Lumsdon arrived in support to take his pass inside and whip the ball across into the box for Hawley to hit a half-volley just inside the post.
Cheltenham made two changes at half-time and from a JJ Melligan free-kick Kayode Odejayi had a header turned round the post by Zigor Aranalde.
But it took a super fingertip save by Higgs to prevent Carlisle going further in front, when he dived full stretch to turn a Holmes close-range shot round the foot of the post.
Caines almost helped himself to a goal in the 88th minute when Melligan found him unmarked, five yards out with a free-kick.
Westwood left him shaking his head in dismay by first blocking his header and then spreading himself on the line to turn away the Cheltenham man's point-blank follow-up shot.
And in the 90th minute Higgs went full stretch to keep Hawley out with a one-handed push around the post.