Billy Clarke made it four goals in his last five games with a second-half double as Reds came from behind to win a thriller at the Checkatrade.com Stadium.
The Irishman's 81st minute strike from 20 yards capped an exciting second half when there were five goals, two red cards and a penalty.
Reds moved up to sixth as a result of their second successive win in front of a season's-best crowd of 3984.
Richie Barker made two enforced changes with James Hurst and Mark Connolly coming in and Josh Simpson moving into central midfield.
A rugged, physical but effective Gillingham side made for a sharp contrast in styles but Reds should have been in front by the break.
Nicky Adams twice went desperately close. One shot hit defender Leon Legge and another was superbly saved by Gills' man of the match Stuart Nelson.
The visitors' boss Martin Allen pulled off Bayo Akinfenwa after 30 minutes but reverting to a 4-5-1 formation actually made the visitors harder to break down, although they rarely tested Paul Jones before the break.
But the second half exploded into life straight away when Mark Connolly brought down Danny Kedwell as the striker tried to turn him and after due consideration ref Steve Rushton pointed to the spot. KEDWELL smashes the penalty home to the delight of the visiting fans.
It looked like becoming a bad afternoon for Reds a few moments later when Gary Alexander tangled with Legge on the far side. Alexander, who was booked in the first half, was shown a straight red for violent conduct and Reds were down to ten men.
So were Gillingham a few moments later when Charlie Lee picked up a second yellow for a foul on Nicky Adams and from the free kick Reds levelled on 53 minutes. Adams' free kick was meant to set up Clarke for a shot at goal but all he could do was head it on to McFADZEAN who volleyed it past Nelson.
Now Crawley had the bit between their teeth. Clarke and Simpson were inches off target before the hosts went in front on 65 minutes. Adams' free kick from 20 yards hit the outside of the post and bounced out and CLARKE turned to fire home from a tight angle.
But the lead lasted just three minutes. Reds failed to cut out Myles Weston's cross from the right and LEGGE stuck out a foot and the ball rolled past a wrong-footed Paul Jones.
It was anyone's game at that stage but the closing stages were dominated by Reds. Nelson made outstanding saves to thwart Andy Drury and Jamie Proctor before CLARKE picked up the ball, ran at a retreating defence and then curled a wonderful right-foot shot into the top corner.
There was one more scare for Reds when Jones pawed the ball away after McFadzean's attempted clearance had come back off the post, but apart from that Reds saw out the game with a degree of comfort and the home fans gave the side a deserved standing ovation after six minutes of stoppage time.