First-half goals from Dennis Lawrence, Rory Fallon and Andy Robinson had already made sure Neil McDonald's side would be going a third game without a win even before the break.
But more strikes from Darren Pratley and a second from Fallon ensured the Swans soared back into the top six in convincing fashion.
And it couldn't have come at a better time for Kenny Jackett who has come under pressure to turn around the Welshmen's fortunes.
But he must have known it was going to be his day after just 28 seconds when injury-hit Carlisle were carved open as Pratley crossed for Fallon and the Kiwi striker was only denied an acrobatic opener by a top save from Keiren Westwood.
But Westwood was beaten just seven minutes later when Robinson's pass while sitting on the floor set up Lawrence to head home the opener.
Leon Britton, Lee Trundle and Robinson all went close before Fallon kept the onslaught going on 15 minutes when he converted Pratley's cross from inside the area.
And as the chances kept coming it was a matter of time before number three came and Robinson burst through the middle of the park before letting fly from 30 yards with a superb striker which left Westwood standing and admiring.
Kevin Gall did offer Carlisle some hope on 34 minutes when he broke free and his curling shot had Willy Gueret beaten, only to see the shot come back off the woodwork.
But Swansea were unable to add to their tally before the break despite Fallon, Trundle and full home debutant Ian Craney all trying their luck.
Yet captain Pratley kept the goals coming when he finished off a delightful Swans move on 59 minutes to cap a fine individual performance.
Fallon made it five three minutes later when Trundle couldn't finish a silky run and allowed his partner to scramble home from a few yards out.