Kevin Street struck the winner 13 minutes from time to condemn the Reds to defeat in what could be their last ever home game.
Crawley's future will be decided on Wednesday when the creditors vote whether to liquidate cash-strapped club.
Robin Gibson had a shot from the edge of the box well handled by keeper Ben Hamer earlier on.
Rangers striker Guy Madjo then blazed over after he was put clean through on goal and he also saw an opportunist 35-yard volley fly just over with Hamer well beaten.
However, there was no surprise when Rangers broke the deadlock on 40 minutes following a deflected free-kick by Neil Grayson.
The ball bobbled around the Crawley six-yard box and Nathan Talbott was on hand to slot under Hamer from close range.
Jake Edwards almost hit back immediately for the Reds with a shot that was parried wide by Dean Williams and Ben Judge hit the equaliser within seconds.
The defender was first to react to a blocked header by Edwards from a Lee Blackburn corner and powered home into the bottom corner from six yards.
Blackburn went close to adding another ten minutes later following a scuffed clearance by Williams. It landed straight at the feet of the midfielder and he lobbed just over from the edge of the box.
Rangers also threatened before the break, first through a header by Grayson which fell just wide and then from a shot by Madjo which was straight at Hamer.
The visitors went close again early after the restart through the lively Talbott. He was found in yards space on the left and hit an angled drive that Hamer did well to tip over in the bar.
Grayson and substitute Delapo Olaoye squandered further chances for Rangers, before Street settled the game.
Gibson's low piledriver was deflected into his path and he made no mistake with a sidefooted finish from six yards.
Crawley piled on the pressure in the latter stages in search of a leveller, but they were restricted to long-range efforts from Blackburn and Michael Bostwick.
Defeat keeps Crawley bottom of the table with minus one point, while Rangers remain in dreamland alongside some of the biggest clubs in the Conference.
Crawley's future will be decided on Wednesday when the creditors vote whether to liquidate cash-strapped club.
Robin Gibson had a shot from the edge of the box well handled by keeper Ben Hamer earlier on.
Rangers striker Guy Madjo then blazed over after he was put clean through on goal and he also saw an opportunist 35-yard volley fly just over with Hamer well beaten.
However, there was no surprise when Rangers broke the deadlock on 40 minutes following a deflected free-kick by Neil Grayson.
The ball bobbled around the Crawley six-yard box and Nathan Talbott was on hand to slot under Hamer from close range.
Jake Edwards almost hit back immediately for the Reds with a shot that was parried wide by Dean Williams and Ben Judge hit the equaliser within seconds.
The defender was first to react to a blocked header by Edwards from a Lee Blackburn corner and powered home into the bottom corner from six yards.
Blackburn went close to adding another ten minutes later following a scuffed clearance by Williams. It landed straight at the feet of the midfielder and he lobbed just over from the edge of the box.
Rangers also threatened before the break, first through a header by Grayson which fell just wide and then from a shot by Madjo which was straight at Hamer.
The visitors went close again early after the restart through the lively Talbott. He was found in yards space on the left and hit an angled drive that Hamer did well to tip over in the bar.
Grayson and substitute Delapo Olaoye squandered further chances for Rangers, before Street settled the game.
Gibson's low piledriver was deflected into his path and he made no mistake with a sidefooted finish from six yards.
Crawley piled on the pressure in the latter stages in search of a leveller, but they were restricted to long-range efforts from Blackburn and Michael Bostwick.
Defeat keeps Crawley bottom of the table with minus one point, while Rangers remain in dreamland alongside some of the biggest clubs in the Conference.