Goals in each half by Alfie Pavey and Anthony Jeffrey put Dover in control before Matty Kosylo got one back for the visitors.
Town were below par, lacking the zip and incisiveness evident in the recent wins over Eastleigh and Barnet, although they were also missing influential duo James Ferry and James Hardy.
Dover battled well, showing they are up for the fight to survive, but Town struggled to get into their stride.
The visitors were better with the ball on the deck, getting the likes of Cameron King and Devante Rodney into the action around the Dover box, with The Shaymen getting little joy from high balls against Dover’s tall centre-half Kevin Lokko.
The hosts created some early half-openings, with Sam Johnson saving tame efforts by Bedsente Gomis and Jeffrey.
The Town keeper then punched away Mitch Brundle’s free-kick before reacting well to hold Stuart Lewis’ follow-up from the edge of the box.
Halifax’s first chance then followed when a flick-on by Scott Quigley - one of three changes along with King and James Berrett - was met by Rodney’s low shot across goal, which was tipped behind by Lee Worgan.
But Dover’s opening goal, when it arrived, was probably deserved on the balance of play, with Jai Reason showing some neat footwork before his low pass across the box was tapped in by Pavey.
Halifax were left protesting about Raison’s use of his arm in the build-up to the goal, but to no avail, with Kosylo booked for dissent.
Niall Maher, who had started on the right of the midfield diamond, swapped places with Berrett at its base, but it looked like it would need more of a change than that for Town to impose themselves on the match.
For once, a ball into the box wasn’t headed away by the dominant Lokko, and Rodney was able to cut the ball back to Kosylo on the edge of the box, but his shot, under pressure, was dragged well wide.
Reason had been influential for the hosts, linking play effectively and finding pockets of space in the final third, although ‘handy’ might have been how Halifax would have described the midfielder’s contribution.
The wind hadn’t helped either side, but Town were too disjointed in attacking areas to exert any pressure; half-time came at a good time for them to reassess.
Quigley had a go from 25 yards shortly after the restart, but it was comfortably held by Lee Worgan.
That was after Jeffrey had cut in from the left and seen his low shot held by Johnson.
A terrific cross-field pass by Berrett then sent Kosylo away, and after cutting in from the left, Worgan kept out his drilled shot from just inside the box.
Pavey fired just wide for Dover after a free-kick had bobbled around in the Town box, before Maher’s header from a corner was easily saved.
Dover were then gifted a second when Jeffrey’s right-footed cross from the left was left by the Town defence and Sam Johnson, and nestled into the far corner.
Halifax were then gifted one straight back as Brundle left a long kick up-field, allowing Kosylo to nip in and head the ball over the on-rushing Worgan, and the ball bobbled into the unguarded net.
Town the broke quickly after regaining possession on halfway and King played in substitute Manny Duku to the right of the box, but the striker was off-balance as he sent the ball wide from 18 yards.
The Shaymen were now applying the pressure, playing with more urgency, as Dover began to lose their fluency.
New loan signing Ryan Gondoh was handed his debut late on, and looked a bundle of energy, but Halifax never really came close to an equaliser.
Dover: Worgan, Lokko, Brundle, McNamara, Taylor, Reason, Jeffrey (Doe 88), Lewis, Gomis, Pavey (Effiong 80), Allen (Nortei 89). Subs not used: Passley, Daniel.
Scorers: Pavey (25), Jeffrey (61)
Shots on target: 8
Shots off target: 6
Halifax: Johnson, Duckworth, Clarke, Brown, Skarz, Maher, Berrett (Gondoh 84), King, Kosylo, Rodney, Quigley (Duku 69). Subs not used: Rowley, Staunton, Preston.
Scorer: Kosylo (65)
Shots on target: 5
Shots off target: 5
Referee: Simeon Lucas
Town man of the match: Matty Kosylo