Carlisle, winners of only four games since the turn of the year, edged the opening exchanges and David Amoo had a shot blocked before a David Symington cross was turned over the bar by keeper Paul Jones.
Winger Andy Drury threatened for Crawley with a low rasping shot which keeper Jordan Pickford pushed around a post.
Pickford did well again to dive to his left to keep out a low goal-bound shot from striker Matt Tubbs.
United had a let off when a defensive slip by Reece Brown let in Jamie Proctor and his angled shot flew over eight minutes before the interval.
Proctor was off target again after defender Mark Connolly provided a teasing cross to the back post just after the break.
Carlisle came close to breaking the deadlock after 57 minutes when midfielder Liam Noble’s shot rattled the crossbar.
United’s Brad Potts later drove into the side-netting before Noble’s goal-bound shot was saved.
Tubbs, put through by Proctor, should have hit the target for Crawley when blazing over in an even contest.
Proctor might have snatched victory in stoppage time but his shot was well saved by Pickford.