But it was Cambridge who started most brightly with Robbie Simpson fired a difficult volleyed chance on the turn well over the bar in the opening minute to serve notice of his intent alongside `debutant' striker Marcus Richardson.
Mark Roberts was forced to awkwardly knee the ball over his own bar soon after as the ball pinged in the air off the head of Cambridge's unsuspecting Rob Wolleaston following a right-wing cross from Stephen Smith.
Halifax were on the defensive again when a free-kick by Courtney Pitt was glanced just wide of the far post by Michael Morrison.
But it was the visitors who took the lead after 14 minutes thanks to a header by Roberts from 12 yards as he beat already committed keeper Paul Crichton to the ball.
The action moved back up the other end soon after with Pitt firing narrowly wide from 18 yards after Richardson had accidentally handled the ball during the move.
Cambridge's Jon Brady earned the first yellow card of the game for a rash challenge on Jake Wright in the 22nd minute, but Halifax could make nothing of the resulting free-kick.
Pitt followed his team-mate into the book six minutes later for a foul on Gus Uhlenbeek, which seemed more in frustration than malice.
Halifax continued to take the initiative in attacking and were unfortunate to see Andy Campbell's diagonal drive from the left side of the box go past the back-post around the half-hour mark.
Halifax's Danny Forrest fired wide from the edge of the area after twisting past Tommy Jaszczun, while Lewis Killeen forced Crichton into making a good stop just before the break.
And there were boos at half-time from the home fans disappointed with United's display after a bright start.
The second half did not start much better for the hosts as Morrison, who has been called up to the England National Game XI for their friendly at Forest Green, was forced to clear behind a dangerous cross from Martin Foster early on.
Crichton was twice called into action soon after as first Killeen fired a drive from 20 yards and Forrest tried his luck from similar range.
Foster curled a free kick around the wall but straight into the hands of the Cambridge keeper in the 55th minute.
United manager Rob Newman had seen enough and made a double change with Josh Simpson and Michael Gash coming on for Smith and Wolleaston with Cambridge going three up front.
It inspired the hosts to have their best attack yet with Pitt seeing a low 25-yard pile-driver hit the post and Robbie Simpson having his shot on the rebound blocked by a defender.
But just when the pattern of play seemed to be going Cambridge's way, Halifax extended their lead after 66 minutes with Adam Quinn having a free header from Foster's corner from the right.
Foster fired just wide from the edge of the box soon after as gaps again emerged in the United defence. Gash held his head after his header from 18 yards hit the bar following a left-wing cross from Jaszczun after 73 minutes.
But Halifax again came close as Roberts nodded another Foster corner just narrowly off target.
Foster went into the book for taking a free-kick too early eight minutes from time and ended up blasting it over the bar when he finally took it.
Cambridge nicked a consolation in the final minute as Jaszczun blasted home from 35 yards, but it was too little too late.