Graham Kavanagh's goal gave Carlisle a second successive home win and deepened Cheltenham's relegation fears.
Cheltenham were almost gifted the lead just before the break when Alan Wright's long ball was headed against his own bar by Richard Keogh.
After the break, Keogh hit the opposition's bar when he missed a great chance to open the scoring.
But Carlisle got the winner when Simon Hackney's cross was spilled by Brown and Kavanagh slammed in the loose ball.
Carlisle: Krul, Raven, Livesey, Keogh, Liddle, Taylor, Thirlwell, Kavanagh, Bridge-Wilkinson (Welsh 88), Hackney, Graham.
Subs Not Used: Williams, Gowling, Bridges, Madine.
Booked: Kavanagh.
Goals: Kavanagh 64.
Cheltenham: Scott P Brown, Bird, Diallo, Gallinagh, Wright (Spencer 80), Murray (Vincent 57), Montrose (Payne 86), Westlake, Ridley, Hammond, Connor.
Subs Not Used: Higgs, Kenton.
Booked: Vincent.
Att: 5,374
Ref: Karl Evans (Greater Manchester).
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