Steve Prescott's 81st minute drop-goal ended Hull's slump and took them to fourth place in the Super League.
They twice trailed by 10 points in this classic, but snatched the win when Prescott was on target from 40 metres out.
With the match delicately poised, Martin Moana's tackle kept out Richard Horne to preserve Halifax's lead, until 11 minutes from time, when Jason Smith, Horne and Tony Grimaldi combined for Chris Smith to cross in the corner. A penalty given against Scott Logan for dissent after David Maiden had lost the ball allowed Bloem to level the scores.
Halifax were a team inspired early on, taking the lead when an astonishing Shayne McMenemy pass sent Ollie Marns over in the corner. Their second try came when Daryl Cardiss took advantage of Hull's hesitation from Gavin Clinch's kick-through, after Cardiss himself had begun the attack by running back an unusually poor kick from Jason Smith.
The Hull loose-forward soon made amends: in the space of three minutes he set up a try for his namesake, Tony, and then scored one himself, twisting out of tackles to put his side level.
It did not stay that way for long, the two penalties from Bloem and a second try from Cardiss consolidated their position, but Hull hit back with an effort from Gareth Raynor and they were ahead by half-time thanks to Steve Prescott's try and goal.
Halifax: Cardiss; Marns, Donlan, Hassan, Gibson; Dunemann, Clinch; Goldspink, Lawless, Hobson, Bloem, Davidson, McMenemy. Substitutes used: Penkywicz, Moana.
Hull: Prescott; C Smith, Campbell, Bird, Raynor; Horne, T Smith; Felsch, King, Broadbent, Maher, Grimaldi, J Smith. Substitutes used: Maiden, Jackson, Craven, Logan.
Referee: S Cummings (Widnes).