United had to settle for a point from a game in which they appeared to be in control having taken a two goal lead thanks to some excellent football.
It was a frustrating day, as Crawley bit back in the second half, with the share of the spoils leaving Carlisle four points shy of the play-off places.
United pressed well from the kick off and they stole possession from a loose pass from McNerney as they left their opponents with no room to breathe. A high delivery from Liddle followed but the whistle blew as Bennett raced in to challenge Morris.
Crawley replied with a quickly taken free kick which saw Ahearne-Grant use his pace to get down the left flank. He won a corner when his cross bounced off Liddle, but that was too deep and the hosts were able to clear.
The Blues created another half chance when Jones swung a high cross into the mix. Nadesan tried to flick it for Hope to strike but there was just too much on it and it bobbled harmlessly behind.
A cross from Parkes from the left flank brought a header from Nadesan but it was difficult to add power and it was comfortable for Morris to claim.
An acrobatic fall to the floor from Evina earned his side a free kick at the other end, but that was wasted and it gave the home side the chance to break. Devitt strode out of defence and his pass invited Lambe to go through on goal. A heavy first touch allowed Crawley to recover and the moment was gone.
Carlisle appeared to be clean through again when Bennett flicked on a good pass from Parkes, and Hope beat his man with ease to get to the byline. He had options, but he was off balance and his pass went behind the advancing blue shirts.
United pushed and probed and Bennett showed good control to take a ball over the top in his stride. He spun, and fed it to Hope, but his initial drop of the shoulder and snapshot was blocked. He picked up the loose pieces and beat his man again, but his drive took a touch off the defender and the save was easy for Morris to complete.
Crawley had their moments, and a shot from the edge of the area from Payne had to be charged down by Hill as the away side enjoyed a decent spell. Evina and Boldewijn had crosses from wide on the left which had to be cleared, but it was the home side who deservedly took the lead with a wonderful finish from Richie Bennett.
A crossfield pass from Devitt left the unmarked forward with time to weigh up his options, as he took it on his chest on the angle of the box, and he left Morris with no chance as he swept an unstoppable goal of the season contender into the bottom corner.
Incisive football from Hope put him clean through in time added on for the half when he exchanged passes with Lambe and Devitt in an advanced position. A clipped pass from Lambe left the wide man with a difficult header, but he couldn't quite squeeze it past the diving Morris.
It took just 55 seconds of the second half for Carlisle to double their advantage when a cross from Nadesan caused all kinds of problems. Morris couldn't keep it in his hands, and he could only parry as Bennett tried to stab it in. The rebound came back to Bennett, and he kept a calm head to tee it up for a cross from Devitt. Hallam Hope was eventually able to celebrate goal number 12 of the campaign when the assistant referee signalled that his header had dropped over the line.
The Red Devils tried to get a foothold in the game and a good spell following the goal was complemented by a decent finish from Ahearne-Grant as he twisted and turned on the edge of the area. He found the slightest of gaps and buried a low shot past Bonham's dive.
United missed a great chance to open the gap once again when Bennett beat the offside trap to take the ball into the area. He squared it for Nadesan but it had just too much on it and Morris was able to spread himself and block when the shot came in.
The Crawley equaliser was a gift for the Red Devils as Ahearne-Grant let fly with a speculative effort from 25-yards. Bonham misjudged it and it squirmed out of his grasp and over the line.
Jones was a whisker away with a curling thunderbolt as Carlisle tried to reassert themselves, and an Ellis header from a Lambe corner sailed over the bar when the clock ticked into time added on.
Carlisle United - Bennett (37), Hope (46)
Crawley Town - Ahearne-Grant (56 & 82)
Carlisle United - Hill (45), Parkes (46), Hope (60)
Crawley Town - Boldewijn (59)
Carlisle United - Bonham, Liddle, Ellis, Hill, Parkes, Lambe, Devitt (Joyce 64), Jones, Hope, Bennett (O'Sullivan 70), Nadesan (Twardek 77). Subs - Gray, Grainger, Brown, Stockton.
Crawley Town - Morris, Young, Payne (Tajbakhsh 70), McNerney, Connolly, Boldewijn, Smith, Ahearne-Grant, Evina, Bulman, Randall (Camara 54). Subs - Mersin, Cox, Djalo, Lelan, Sanoh.
Referee - Martin Coy
Attendance - 4,097 (75 away fans)