The Cumbrians paid the price for a lack of composure in front of goal as Danny Cadamarteri, on-loan Watford striker Joe Garner and James Berrett all went close.
It was a great individual piece of skill by Crawley's Nathan Byrne which broke the deadlock in the 62nd minute.
The on-loan Spurs full-back jinked his way through the heart of the Carlisle defence before neatly slipping the ball into the bottom corner.
There was a touch of fortune about Crawley's second goal in the 73rd minute when Nicky Adams let fly from 30 yards and his shot took a huge deflection off defender Danny Livesey before looping over the head of wrong-footed Carlisle goalkeeper Mark Gillespie.
Garner and substitute Mark Beck went close with late headers for the home side, but Carlisle's attempts to stage a recovery fizzled out.