United claimed a much-deserved three points courtesy of Sam Lavelle's header at Burton Albion.
The centre back's first half goal sealed the victory for the Blues, who had chances to extend their advantage during a solid away performance.
But the Cumbrians also had to defend diligently throughout and were rewarded for a strong rearguard display with a clean sheet to accompany the vital win.
Paul Simpson made two changes from the side that suffered a narrow defeat at Bristol Rovers last time out, and they both came in the backline - as Paul Huntington and Jack Ellis stepped into the starting line-up.
The duo replaced Jordan Gibson and Fin Back, with the latter dropping out the squad entirely as Jack Robinson returned to the bench.
It was the Blues who had the first chance of note in the third minute. Jack Diamond had time and space to line-up the shot from 25 yards, with his swerving effort parried by Max Crocombe and then cleared before a blue shirt could connect on the rebound.
Jack Ellis was then inches away from connecting with Mellish's tempting cross after finding space at the back post as United enjoyed a strong start.
But Burton grew into the game and the visitors had to stand strong to defend a string of long throw-ins - while Harry Lewis was forced into a fine stop to tip John Brayford's close range header over the bar as the Brewers built some momentum.
And having survived that scare, Carlisle took the lead just after the midway point of the first half.
A foul on Jack Armer handed the Blues a free-kick in a promising position and Taylor Charters took responsibility, sending in a teasing delivery that was glanced home by Lavelle for his second goal of the season.
The Cumbrians continued to push forward and, after Diamond saw a shot deflected wide of the near post, he turned provider - sliding in Jack Armer whose drilled cross was well claimed by Crocombe before Luke Armstrong could apply the telling touch.
Joe Powell then fired high and wide for Burton from 30 yards as they targeted a response, and Martin Paterson's side began the second half brightly.
Long throw-ins were once again proving a useful attacking outlet and Lewis had to smartly save after one such set piece fell kndly to Deji Oshilaja - his powerful shot on the spin repelled by the visiting stopper before substitute Bobby Kamwa saw a placed shot held moments later.
United remained a threat though and Diamond had Crocombe at full stretch as his rasping drive from 25 yards was only kept out by the 'keeper's fingertips.
After making some attack-minded changes, it was Burton who applied much of the pressure in the latter stages of the game.
But they failed to seriously test Lewis as the Carlisle backline stood strong through four minutes of injury time - which included a fine block from Huntington to stop a goalbound Kamwa strike creeping in - to seal a first win since January 1.
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Goals
Carlisle United - Lavelle (27)
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Bookings
Carlisle United - Diamond (12), Vela (86)
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Teams
Burton Albion - Crocombe, Brayford (Hugill 72), Oshilaja, Sweeney, Powell, Bennett (Hackford 17), Helm (Kamwa 58), Ola-Adebomi, Bola (Seddon 58), Hamer, Nsiala. Subs: Blackman, Harper, Carayol
Carlisle United - Lewis, Armer, Lavelle, Huntington, Charters (Robinson 82), Ellis, Mellish, Diamond (Butterworth 82), Neal, Armstong, Vela (McCalmont 88). Subs: Breeze, Gibson, Robinson, Maguire, Grehan
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Match officials
Referee - Craig Hicks
Assistant Referee 1 - Kenwyn Hughes
Assistant Referee 2 - Christopher Husband
Fourth Official - Paul Stonier
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Attendance – 2,247 (246 away)