Niall Maher's late goal was not enough for Halifax as defeat at 10-man Havant extended their winless run to nine games.
The Hawks, meanwhile, ended their 10-game unbeaten run in midweek and goals from Tyler Cordner and Alfie Rutherford ensured back-to-back wins.
Cordner got the first goal of the game, and his second in a week, three minutes into the second half as he headed past goalkeeper Sam Johnson.
Rutherford doubled the lead when Brad Tarbuck slid in a cross from the right and the forward knocked the ball into an empty net.
Maher pulled one back, but Halifax were unable to find an equaliser, despite a late red card for Havant defender Will Wood.
Match report supplied by the Press Association
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