Carlisle's hero was their former striker Gary Madine, who marked his first home appearance since rejoining on loan from Sheffield Wednesday with a sparkling performance capped with the decisive first-half goal.
Madine was the home side's main threat from the start, forcing a brilliant save from Wes Foderingham with a thumping header from James Berrett's corner.
He grabbed Carlisle's first goal in four home games in the 38th minute, turning to slot a low right-footed shot past Foderingham from six yards after a driving run by Brad Potts, who cut the ball back to the striker from the right of goal,
Swindon had to be content with a couple of speculative long-range efforts from Jack Stephens and Michael Smith as they failed to make the most of their first-half possession.
But Robins showed a more direct approach after the break and it took a combination of good work by Jordan Pitchford and some weak finishing to prevent an equaliser.
The goalkeeper was alert to turn away an Alex Smith free-kick then Michael Smith and substitute Alex Pritchard both fired shots straight at Pitchford when they might have done better.
Carlisle had to play the final minute of added time without Berrett, who was sent off for a second yellow card after fouling Louis Thompson.