A first-half goal from Reuben Reid handed Cheltenham a 1-0 win which ended Carlisle's run of five games without defeat.
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The win put Town's promotion drive back on track after failing to win any of their previous six away games.
Cheltenham were quick to turn an early Carlisle corner into a dangerous counter-attack as Ryan Broom's curling pass fed in Alfie May but Adam Collin was alert and advanced from his goal to block May's shot.
The Robins were again threatening from Chris Hussey's right-wing corner but Reid, moving in at the far post, slammed his header into the side-netting.
The visitors were making light of the difficult conditions and Hussey had their next big chance, forcing Collin to make a full-length save as he cut in from the left.
Cheltenham's bright start was rewarded with a 26th-minute goal with Hussey playing a major part, whipping in a free kick from the left which Reid was on hand to fire home from close range at the far post.
Carlisle were unable to harness the wind at their backs in the first half and saw a Nathan Thomas free-kick from a promising position fly high over the bar.
Carlisle fared better after the break and Omari Patrick worked himself space only to clear the bar with his shot.
May replied for Cheltenham with a measured effort from the edge of the box which Collin got both hands to in conceding a corner.
As the Cumbrians fought for an equaliser, forcing Town goalkeeper Owen Evans twice to get down well to grab crosses from Jack Iredale, they suffered a blow when new signing Callum Guy was stretchered off.