The Shaymen are among five teams separated by only two points in the race for sixth and seventh spots with only one game remaining.
Maidenhead midfielder Ryan Upward was shown a second yellow card seven minutes before the break, and Halifax went in ahead after Jake Hyde headed in Luke Summerfield’s corner.
Jeff King added a second from a free-kick in the 58th minute and, although Danilo Orsi-Dadomo quickly pulled one back, Halifax held on.
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