James Berrett was dismissed just after half-an-hour for a poor tackle, but one that looked a booking and no more.
After that, The Shaymen struggled to impose themselves against a Havant side who didn’t make full use of their man-advantage.
The biggest plus for Town is another clean sheet - their fifth in their last six games, with The Shaymen now not conceding in five hours at home.
But at the other end, their problems persist, with one shot on target and not a glut of chances created, although Berrett’s red card hampered that to some extent.
Jonathan Edwards made his first Town start since the return game against Havant back on November 3, joining Scott Quigley up-front in a 4-4-2 - for half-an-hour at least.
He had an immediate chance, volleying high over the bar from a tight angle within the first 20 seconds.
A through ball nearly sent Quigley through on goal but for a crucial interception by Jordan Rose, who was on hand again to crowd Quigley out after another incisive pass. Matty Brown headed the resulting corner wide.
It was a positive start from Town, who were on the front foot and playing with purpose.
Havant’s main outlet was lively right-winger Jack James, who had a goal-bound shot blocked by Matty Brown.
Matty Kosylo cut in from the right and fired a yard or two over left-footed, but Havant had the first efforts on target midway through the first-half - Alfie Rutherford’s shot easily saved by Sam Johnson before Andreas Robinson’s free-kick was held - as the visitors awoke from their sluggish start, thanks in no small part to James’ forays forward.
A few groans were rumbling as Town’s decision-making started to let them down, with Kosylo and then Edwards both failing to make the most of possession in decent areas.
Referee Carl Brook, who was a late replacement for original referee Matthew Dicicco, then took centre stage as he added to his tally of seven red cards in 19 games by controversially sending-off Berrett just after the half-hour mark.
Berrett’s tackle on Theo Lewis was poor, with his foot too high, but a booking would surely have sufficed.
After that, the game started to boil over when the visitors protested that a foul should have been given in their favour for a push near the dugouts before uproar greeted James’ late tackle on Ryan Sellers that earned him a yellow, much to the home supporters’ ire.
James fouled Sellers near the touchline a few minutes before half-time, but was spared a second caution.
But the referee’s decision had ensured he was now the centre of attention, with every adjudication - or lack of one - prompting an angry response by one side or the other.
Town boss Jamie Fullarton waited at the mouth of the tunnel for Brook as he walked off at half-time to speak his mind.
The Shaymen were now in a 4-3-2 system, with Niall Maher sitting in-front of the back four.
But the visitors started the second-half well, helped by substitute Hassan Jalloh, who burst to the edge of the box before his tame effort was straight at Johnson after Lewis had sent an overhead kick over the bar.
Robinson then saw his shot drop wide from outside the box, with Town being pressed back.
Kosylo, playing more centrally now, embarked on a superb driving run before firing low across goal and wide left-footed.
But the 10-men found it difficult to produce any fluidity or intensity to their play; Scott Quigley showed good skill to evade a tackle and then burst towards the box, but a heavy touch saw the chance evaporate.
Havant’s earlier pressure had abated, although Joe Quigley’s header from a corner was well blocked.
Neither team covered themselves in glory as the game went on, certainly from an attacking sense, as ideas and invention were in short supply in a desperately poor finish, although Town defended with resilience and discipline.
Both sides could have won it at the death though, as substitute Jordan Preston saw a rasping drive tipped over before Wes Fogden miscued a cross only yards from goal.
Halifax: Johnson, Duckworth, Clarke, Brown, Sellers, Berrett, Maher, Kosylo, Hardy (Ferry 68), Edwards (Preston 76), S Quigley (Staunton 80). Subs not used: Rowley, Hanson.
Shots on target: 1
Shots off target: 8
Havant: Dudzinski, Strugnell, Williams, Fogden, Lewis, J Quigley (Paterson 76), Robinson (Paul 66), Rose, James (Jalloh 46), Rutherford, Cordner. Subs not used: Woodford, Sekajja,
Shots on target: 5
Shots off target: 10
Referee: Carl Brook
Town man of the match: Matty Brown