Carlisle were dealt a cruel blow as they had victory ripped out of their hands with almost the last kick of the game on a day when they had worked so hard to get into a winning position.
Crawley sparked an attack from nothing in the opening minute when a 40-yard crossfield pass was well controlled by Cox. His next touch was to drill a the ball to the back stick but Raynes got in the way to head it clear.
The game tightened up but another raking pass, this time from right to left, gave Boldewijn the chance to run at Grainger. He dropped a shoulder to get the delivery in but Collins couldn't guide a difficult header at the target and Gillesphey helped it on its way to safety.
United started to find their passing boots and good work from Ibehre gave Devitt options on the edge of the box. He went for a curling shot and Morris was relieved to see it bounce back off the post as it flew over his dive. Grainger was quickly onto the loose ball but his first time volley flew wide of the upright.
Carlisle looked confident and Ibehre timed his run to get past the back line and cut it back into the penalty area as he latched on to a ball over the top. Proctor watched it onto his boot but a poor connection meant his shot was always heading wide.
Crawley soaked up the pressure and hit back with venom when Collins shielded a pass with his back to goal. He was allowed to turn and it suddenly opened up in front of him, inviting the shot. He accepted the invitation and stroked an unstoppable drive into the top corner.
Carlisle looked for a response and Ibehre had a goal chalked out as Morris fell to the floor when a high ball came into the box. Lambe was next to try his luck with a low shot from distance which flew through legs. Morris had to take care as he pulled it into his chest.
An already tough ask became a very difficulot job when Collins waited for a miscued high ball to drop inside the area. Keeper Mark Gillespie raced off his line to try to get a punch but the referee wasted no time at all in pointing to the spot as the big striker toppled to the floor. Collins dusted himself down to finish the spot kick off with a cruncher which zipped into the bottom corner.
Carlisle were right back in it moments later when Grainger lifted a pass over the top in search of his strikers. The in-form Jabo Ibehre was left with just the keeper to beat and he did everything right as he took a touch before clipping his fourth goal in four games into the waiting net.
The visitors should have been back on level terms with their very next attack when Lambe surged through two challenges from inside his own half. The keeper held his ground and the wide man was disappointed to see his rasper angle over the bar.
Carlisle didn't allow their heads to drop and they equalised just before the break when Liddle came up in support of the attack. His cross was perfect and former-Red Devil Jamie Proctor jumped high to nod a blistering header past substitute keeper Yusuf Mersin.
And the Blues almost took the lead deep into time added on for the half when Ibehre was fouled just outside the box. Grainger placed it but was a whisker away with a dipping free kick which dropped just over the bar.
Carlisle were on the front foot from the kick off of the second half with balls into the box from Devitt and Proctor which tested the home defence. But it was Cox who had the first shot on target when he stayed wide for a ball into the area. It eventually came to him but he put a grass-cutter right at Gillespie.
Another Lambe cross had Proctor interested at the other end but he was closely marked and his header rose high into the air. Ibehre tried to shield it but he was quickly closed down.
The Cumbrians probed down the left wing, with Proctor and Grainger right in the thick of it, but Crawley defended in numbers to keep the danger at arm's length.
But the Red Devils could do nothing about a wonderful defence splitting pass from Proctor which left Lambe one-on-one with Mersin. A touch with his toe left the stopper on the floor and all that was left to do was to make sure that it crossed the line and hit the back of the net.
United dominated the possession and the territory as they peppered the box with crosses, with Devitt and Lambe always an outlet, but goal mouth scrambles and ricochets went the way of the hosts as they looked to stay in touch.
Smith had a rare clear cut chance when it sat up in front of him from a half cleared corner but it was United who looked the more likely to add to the tally as they continued to rule the roost. But Payne almost dealt a sucker punch when he volleyed from just oustide the area. Gillespie was beaten but relieved to see it hit the side netting.
Crawley got themselves in a mix as they took an age to clear late in the day and Joyce pulled the trigger when he spotted the keeper off his line. It took a deflection and screwed past the upright.
Payne had another volley whip straight at Gillespie from a half cleared set piece, and a header from Collins looped onto the roof of the net through a late good spell, but it was left to Smith to grab the share of the points when he volleyed a crisp finish past Gillespie from very close range.
Crawley Town - Collins (12 & 25 pen), Smith (90)
Carlisle United - Ibehre (29), Proctor (42), Lambe (59)
Crawley Town - Smith (45), Yorwerth (45)
Carlisle United - Gillespie (25), Lambe (71), Bailey (85), Ibehre (87)
Crawley Town - Morris (Mersin 32), Young, Payne, Connolly (Yorwerth 27), Boldewijn, Smith, Blackman, Collins, McNerney, Djalo (Roberts 69), Cox. Subs - Harrold, Clifford, Lelan, Murphy.
Carlisle United - Gillespie, Liddle, Raynes, Gillesphey, Lambe (Brisley 89), Bailey, Joyce, Grainger, Devitt (O'Sullivan 83), Proctor (Tomlinson 75), Ibehre. Subs - Crocombe, Adams, S Miller, Nabi.
Referee - Mr Darren Deadman
Attendance - 2,003 (224 away fans)