Two late goals in two minutes from Darryl Duffy and Paul Anderson saw Swansea seal a comeback victory.
Duffy ended his goal drought with a well-taken strike
The home side dominated the first half, but wasteful finishing from Duffy, Andy Robinson and Jason Scotland cost them.
After the break Leon Britton tripped Jeff Smith to concede a penalty, Danny Graham converting from the spot.
But a saved Robinson shot fell to Duffy who got his first of the season from a narrow angle, then Anderson fired in a superb, curling shot from the left.
The win was Swansea's first at the Liberty Stadium this season.
*Anderson's goal was initially attributed to Robinson as it was unclear whether the ball had deflected off the latter's back.
Swansea manager Roberto Martinez will assess the fitness of Joe Allen after he limped off the field.
The match was the Wales Under-21 midfielder's first full league start for the club.
Swansea: De Vries, Austin (Anderson 70), Lawrence, Monk, Rangel, Britton, Pratley, Robinson, Allen (Butler 59), Scotland (Feeney 90), Duffy.
Subs Not Used: Knight, O'Leary.
Goals: Duffy 81, Anderson 83.
Carlisle: Westwood, Raven, Aranalde, Livesey, Arnison, Bridge-Wilkinson, Lumsdon, Thirlwell (Graham 7), Smith, Garner (Murphy 73), Gall (Carlton 85).
Subs Not Used: Howarth, Hackney.
Booked: Lumsdon, Carlton.
Goals: Graham 48 pen.
Ref: Clive Penton (Sussex).