Tony Scully and Lee Blackburn scored in each half to make it two league wins and a draw for the temporary bosses.
Victory further eased Crawley's relegation worries but left Halifax nervously looking over their shoulder. The home side dominated the first half and deservedly took the lead with their first real shot at goal after 17 minutes.
Blackburn broke free down the right flank and crossed for striker Scott Rendell, who missed the ball completely as he tried to shoot. It ran kindly for Scully at the back post and the former Manchester City winger slotted into the bottom corner.
The visitors almost hit back immediately with Lewis Killeen curling inches past the post from the angle of the penalty box.
They went even closer on the half hour when they were denied by a superb double save by Crawley keeper Ben Hamer.
The on-loan Reading keeper blocked a point-blank effort by Nathan Joynes and then recovered to stop the follow-up shot from Killeen with his legs.
Crawley were fortunate to go into the break with the advantage after they were almost punished for some sloppy defending at a corner. Defender Rob Atkinson was left completely unmarked in the six-yard box and somehow scooped over from close range.
From the resulting counter-attack on-loan striker Ryan Peters tested Craig Mawson with a low-angled shot after beating full-back Jake Wright for pace down the right-wing.
Crawley made a change for the second half with big target man Jake Edwards replacing Peters.
The substitute almost made an instant impact when he raced clear of the visiting defence to latch onto Scully's through ball. But Halifax keeper Mawson had read the danger and was quick off his line to punch clear.
The chance sparked a spell of pressure from Crawley and they twice went close before doubling their lead on 55 minutes.
Debutant Mark Wright had a 30-yard drive pushed round the post by Mawson, then Rendell was denied by the visiting keeper with a close-range volley.
However, Mawson could do nothing to stop Blackburn's 25-yard strike which flew through a crowded penalty box and fell into the top corner.
Edwards almost added another just past the hour when he glanced wide from Scully's inch perfect cross.
The Shaymen controlled the rest of the game as they poured forward in search of a lifeline.
Substitute Ryan Sugden almost pulled a goal back 13 minutes from time when he shot straight at Hamer from four yards following good work by Killeen.
Edwards went close again for the hosts soon after with a turn and shot which Mawson did well to get down to smother.
Play quickly switched to the other end and Danny Forrest had a low drive well saved by Hamer with three minutes remaining.
Hamer saved his best stop until last when he tipped over spectacularly from Tom Kearney's 20-yard piledriver.
Victory further eased Crawley's relegation worries but left Halifax nervously looking over their shoulder. The home side dominated the first half and deservedly took the lead with their first real shot at goal after 17 minutes.
Blackburn broke free down the right flank and crossed for striker Scott Rendell, who missed the ball completely as he tried to shoot. It ran kindly for Scully at the back post and the former Manchester City winger slotted into the bottom corner.
The visitors almost hit back immediately with Lewis Killeen curling inches past the post from the angle of the penalty box.
They went even closer on the half hour when they were denied by a superb double save by Crawley keeper Ben Hamer.
The on-loan Reading keeper blocked a point-blank effort by Nathan Joynes and then recovered to stop the follow-up shot from Killeen with his legs.
Crawley were fortunate to go into the break with the advantage after they were almost punished for some sloppy defending at a corner. Defender Rob Atkinson was left completely unmarked in the six-yard box and somehow scooped over from close range.
From the resulting counter-attack on-loan striker Ryan Peters tested Craig Mawson with a low-angled shot after beating full-back Jake Wright for pace down the right-wing.
Crawley made a change for the second half with big target man Jake Edwards replacing Peters.
The substitute almost made an instant impact when he raced clear of the visiting defence to latch onto Scully's through ball. But Halifax keeper Mawson had read the danger and was quick off his line to punch clear.
The chance sparked a spell of pressure from Crawley and they twice went close before doubling their lead on 55 minutes.
Debutant Mark Wright had a 30-yard drive pushed round the post by Mawson, then Rendell was denied by the visiting keeper with a close-range volley.
However, Mawson could do nothing to stop Blackburn's 25-yard strike which flew through a crowded penalty box and fell into the top corner.
Edwards almost added another just past the hour when he glanced wide from Scully's inch perfect cross.
The Shaymen controlled the rest of the game as they poured forward in search of a lifeline.
Substitute Ryan Sugden almost pulled a goal back 13 minutes from time when he shot straight at Hamer from four yards following good work by Killeen.
Edwards went close again for the hosts soon after with a turn and shot which Mawson did well to get down to smother.
Play quickly switched to the other end and Danny Forrest had a low drive well saved by Hamer with three minutes remaining.
Hamer saved his best stop until last when he tipped over spectacularly from Tom Kearney's 20-yard piledriver.