Town took the lead on 9 minutes after an Aaron Brown cross, which was headed in by Carlisle's Chris Lumsdown for an own goal.
Both Royce Brownlie and Christian Roberts missed chances to extend Swindon's lead in the first half. The Swindon defence weren't troubled that often although Carlisle did hit the bar in the first half.
New signing Sofiene Zaaboub came on off the bench replacing the injured Aaron Brown during the first half as well.
Then a minute before half time Carlisle equalised after a corner was headed in by Gray. Paul Evans on the goal line headed the ball out, but it was too late as he was behind the goal line, and the ball hit the bar and rebounded back into the net.
In the second half both sides had a couple of chances, but Swindon had to wait until the 70th minute to take the lead again with Christian Roberts scoring from just inside the box.
Then in the final minute of stoppage time Christian Roberts made sure of the win with another close range goal making it 3-1 to Swindon.
Overall a fairly good game with Swindon always looking the better side, so a 3-1 win was a fair result. Swindon now return to league action as they take on Torquay United away in a Westcountry game next Saturday.