Mousinho, whose goal won promotion for Boro last season, had been on the pitch for only three minutes before netting to move the hosts within one point of sixth-placed Notts County.
Craig Reid wasted an early chance for Stevenage when he could only scoop the ball over the bar from 10 yards after Mark Roberts' deep cross.
The hosts dominated the opening half-hour and Carlisle goalkeeper Adam Collin did superbly to tip away Jamaal Lascelles' point-blank header from Scott Laird's corner.
The Cumbrians then came extremely close after the break when Danny Livesey's downward header from Andy Welsh's corner was just about kept out by the legs of Stevenage stopper Chris Day.
But Stevenage forced the winner with 14 minutes left when Stacy Long's cross-field pass picked out Mousinho and he took a touch before finishing brilliantly via the underside of the bar.