Reds enjoyed their best result as a Football League club after second-half goals from Billy Clarke - his 13th of the season - and Paul Hayes secured a deserved 2-0 triumph at promotion-chasing Sheffield United.
The visitors defended superbly when they had to and always offered a counter-attacking threat. They bided their time and when United made mistakes at the back they were punished by top scorer Clarke and Hayes in the last 11 minutes to send the away fans in a crowd of 18,680 - the biggest to watch Crawley in the league - home happy.
Richie Barker made two changes to the side that drew 0-0 at MK Dons on Saturday with David Hunt replacing Muzzy Dumbuya and Jamie Proctor coming in up front with Paul Hayes dropping to the bench where he was joined by 18-year-0ld Alex Malins, who has just signed his first professional contract.
The Blades were desperate for a win to re-ignite their challenge for automatic promotion but they were frustrated early on by a Reds’ side that settled well into the contest.
The first threat on goal didn’t come until the 24th minute when Matt Hill headed a corner well over but Reds stretched the home side with some neat passing although initially their efforts on goal came from outside the box by Mike Jones, Sergio Torres and Billy Clarke although none troubled George Long in the home goal.
The game came to life towards the end of the first half when both sides could have scored.
Paul Jones got his fingertips onto an angled drive from Ryan Flynn after 41 minutes and it was enough to divert the shot onto the post before David Hunt cleared.
Then seconds before the break Nicky Adams found Billy Clarke four yards out and although he got a firm connection on his header Long made an instinctive save to keep it out.
The Blades came out with renewed vigour at the start of the second half and the visitors had a second let-off in the 49th minute when Michael Doyle's volley beat Jones but struck the post and Hunt again reacted quickly to hack the loose ball away.
But Reds weathered the storm and Torres forced Long to make a save on 57 minutes when a free kick dropped to the midfielder 15 yards out. The visitors threatened again when Clarke's shot appeared to strike an opponent's arm then Adams hit a drive on the run which flew just over.
Substitute Chris Porter wasn't far away when he met a diagonal ball from Dave Kitson with a firm header which he directed wide but Reds continued to defend diligently all over the pitch and with 11 minutes to go they took the lead.
Substitute Paul Hayes robbed Maguire on the right and unselfishly slid the pass into the path of CLARKE who picked his spot from 12 yards.
The goal should have been the signal for a United onslaught but instead Reds doubled their lead in the 85th minute. HAYES robbed Matt Hill 25 yards out and advanced into the box before side-footing past the exposed Long in the home goal. With parent club Brentford desperate to catch United at the top his goal would have gone down just as well in West London.
Reds saw out the game comfortably and at the final whistle the players and management took the acclaim of the 183 fans in a crowd of 18,680.