And not even the second half sending-off of home defender Ryan Toulson with half an hour to go for a second yellow card helped the Red Devils' cause.
By the time Toulson saw red, after racing from the defensive wall at a Crawley free-kick, the home side were firmly in control after Reds conceded two goals in three minutes in the first half, then let in another immediately after the break.
Crawley actually had the first effort of the match after just a couple of minutes, but skipper Tyrone Thompson, who joined Crawley from Halifax in the summer, was unable to convert a cross by Pierre Joseph-Dubois.
Halifax started to dominate and broke the deadlock in the 27th minute after a long ball from the back from Greg Young.
Jon Shaw flicked on and Simon Heslop strode into the area before curling a left foot shot beyond the reach of Town 'keeper Ashley Bayes.
Within three minutes Crawley found themselves two down with Heslop turning provider with a cross from the right and Shaw applying the finishing touch as he swivelled on the edge of the six-yard box and fired home.
Halifax increased their lead three minutes after the break with the impressive Heslop again involved in the build up as he latched onto a Darryn Stamp flick.
He slid in to challenge Bayes, and when the ball rebounded to Anthony Griffith he curled it into an empty net.
Town were reduced to 10 men on the hour when Toulson was shown a red card to become the fourth Halifax player to be sent-off in five league games.
Crawley substitute Mustapha Carayol almost pulled one back when the free-kick was taken, but Halifax 'keeper Adam Legzdins leapt to his left and palmed the ball, which was destined for the top corner, away to safety.
Town dominated the final quarter of the game as Halifax sacrificed a striker to shore-up their defence, but they were unable to break down a stubborn home defence.
Carayol fired wide from a right wing corner and the loan star's cross was sliced clear by Cortez Belle.
Carayol had one final opportunity in stoppage-time, but his shot was not strong enough to trouble the 'keeper.

REDS: Bayes, Bull (Carayol 58), Stevens, Krause, Wilson, Thompson, Bulman, Pinault, Madjo (Nlome-Ndebi 46), Pittman, Joseph-Dubois (Blackburn 46). Unused subs: Watson, Clapham
ATTENDANCE: 1,197