Crawley Town slipped to their third defeat in a row following two first half goals plus a third after the break.
In an exciting see-saw battle, Reds made a great start with an early goal by Dominic Poleon.
Carlisle levelled and then took the lead themselves through goals by Jerry Yates and Danny Grainger from the penalty spot.
Poleon scored his second goal of the game to put Reds on level terms at 2-2 at half-time.
But Carlisle netted the winner a 56th minute winner by Jack Sowerby to take the three points back to Cumbria.
Gabriele Cioffi made just one change to the side which lost 2-0 at Macclesfield with Ashley Nathaniel-George replacing Reece Grego-Cox who was on the bench.
Ollie Palmer served his second match of a three-game ban following his controversial sending-off two weeks ago against Northampton Town.
Mark Connolly was named on the bench having recovered from a torn hamstring which ruled him out of the last four matches.
Reds got off to the perfect start when a long ball through the middle found Dominic Poleon, who controlled the ball well and put the ball in off the post.
However the lead was shortlived as just six minutes later Carlisle equalised in controversial circumstances.
Former Horley Town striker Ashley Nadesan shot powerfully, Glenn Morris saved only for the ball to fall to Yates, who snapped up the loose ball in the six-yard box, despite looking to be offside.
Morris kept Reds in the game with another save moments later, keeping out Yates again when he broke free and again looked to be offside.
Carlisle took the lead in the 37th minute put away by captain Grainger from the penalty spot after George Francomb brought down Yates in the box.
Reds soon got back into level terms and went into half-time at 2-2 thanks to a second goal, by Poleon who received a cross from Luke Gambin and finished well from close-range.
Carlisle regained the lead soon after the start of the second half when Sowerby scored with a first time shot from a pass by Jamie Devitt.
The visitors put Reds under pressure as they pushed for a fourth goal as Devitt forced a couple of great saves from Morris.
Some big shouts for penalties went unheard by the referee and the crowd were impatient with some of his decisions.
Josh Payne drilled a free-kick, the goalkeeper spilled, but the rebound was put behind by Carlisle.
Payne flicked the ball into the area but substitute Reece Grego-Cox couldn't get a clean touch on it and it's straight into the goalkeeper's hands
Crawley Town: Morris, Payne, McNerney, Poleon, Gambin, Francomb, Nathaniel-George, Maguire, Bulman (capt), Camara (Grego-Cox 79, N'Gala
Unused subs: Mersin, Doherty, Connolly, Sesey, Allarakhia
Carlisle United: Collin, Grainger (capt), Liddle, Gerrard, Parkes, Hope, Devitt (Slater 87), Yates, Sowerby, Etuhu, Nadesan
Unused subs: Gray, Miller, Jones, Glendon, Bennett, Campbell
Referee: Nick Kinsley
Attendance: 2,176 (323 away)
Man of the Match: Josh Payne