Halifax started on the back foot as York Uni applied early pressure.
Halifax conceded an unfortunate early goal after a good finish from a York forward. The game then balanced out as Halifax saw a couple of good chances go to waste and had a short corner deflected onto the crossbar.
Another goal just before half time saw Halifax go into the break 2-0 down. Both teams were reduced to 10 men as Jones and the opposite number were sin binned.
Manager Leigh Walker changed the formation in the second half to good effect as a link up between Barron, Jones and Marshall was finished by Jake Bamforth.
Halifax worked hard for an equaliser but then fell behind to another goal. Jones was then dismissed for the second time in the game for a poor stick tackle.
York Uni made the most of their extra man and ended up finishing the game with a further 3 goals from short corner routines.
Halifax could've conceded more was it not for good saves from Metcalfe and Dave Wheatley's strong defensive work.
Man of the match Casey Marshall put in another solid performance in midfield.
Next week Halifax face further away trips to Rotherham in the league and Hull Uni in the cup.