The Shaymen failed to build on an encouraging first-half by conceding twice after the restart through Tyler Cordner and Alfie Rutherford.
Niall Maher got one back for Halifax, but it’s now five defeats and seven draws in the league for Town since that win over Gateshead on August 27.
Jamie Fullarton kept the same side that played against Solihull on Tuesday, and the excellent Matty Brown and Nathan Clarke were resolute in central defence in the first-half, rarely out of position and aerially dominant.
Both sides were composed in the middle third, but just lacked a killer instinct in both boxes.
Halifax came the closest to opening the scoring in the first-half.
A Cristano Ronaldo-esque free-kick by Town’s number seven was brilliantly tipped behind by Havant’s player of the month Ben Dudzinski, before Josh Staunton headed over the resulting corner.
Another Kosylo free-kick was held by Dudzinski shortly afterwards.
From a Kosylo corner, Brown headed the ball back across goal where it was cleared off the line by Will Wood.
Winger Bradley Tarbuck fired just over from an angle inside the area for Havant, who produced some decent build-up play, but failed to register a shot on target in the first-half.
Halifax had seen a few shots blocked by flying Havant defenders, but neither side had come up with the moment of quality needed in open play to break the deadlock.
Those blocked shots were emblematic of the contest, as both sides competed well, closed down, pressed and harried.
But Havant took the lead with their first effort on target just after half-time when a corner was headed high into the air and across goal by Cordner, and dropped down just beneath the crossbar, with Sam Johnson unable to claw it out.
Jonathan Edwards, continuing his positive contribution from midweek with another decent display, played a nice one-two with Cameron King before curling a shot just above the angle of post and bar.
Edwards then won a free-kick, which Dayle Southwell fired narrowly wide, as Town initially responded well to falling behind.
But they were in real trouble when Rutherford tapped-in the influential Tarbuck’s low cross from the right, as Havant found it too easy to carve a route to goal.
The visitors suddenly looked fragile at the back, as Havant now played with real confidence.
Town’s subsequent attacks in trying to get back into the game struggled to yield any clear chances
But, out of nothing, Maher halved the deficit when his innocuous-looking shot from 25 yards was spilled into the net by Dadzinski.
Town’s tails were up after that to set-up a tense climax, in which Will Wood was sent-off for what appeared to be a shove on a Halifax player.
Havant and Waterlooville: Dudzinski, Strugnell, P Robinson, Cordner, Williams (Bradley 60), Tarbuck, A Robinson, Wood, Stock, Rutherford (Cosgrave 77), Pavey (Kabamba 73). Subs not used: Huggins, Woodford.
Scorers: Cordner (49), Tarbuck (64)
Shots on target: 2
Shots off target: 9
Halifax: Johnson, Hanson, Clarke, Brown, Sellers, Maher, Staunton (Odelusi 65), King, Southwell, Kosylo, Edwards. Subs not used: Rowley, Lenighan, Skarz, McLeod.
Scorer: Maher (78)
Shots on target: 5
Shots off target: 9
Referee: Will Finnie
Town man of the match: Matty Brown