Scott Boden netted the decisive goal in the fifth minute but after missing from the spot for Forest Green, James Norwood was dismissed for a late challenge to cap a disappointing night for his team in Yorkshire.
The Shaymen had recorded their first win in six games last weekend and Boden's neat finish from inside the penalty area during the opening exchanges put them on the way to another three points.
Kurtis Guthrie almost headed Forest Green level within two minutes, but Halifax continued to press during the early stages and only a smart double stop from Sam Russell prevented them from extending their advantage.
Forest Green returned for the second half on the front foot and after seeing a header creep over the crossbar, Guthrie struck the post with a snap-shot from inside the penalty area.
Despite holding a slender lead, Halifax were second best but they did offer a brief response through Paul Marshall, who saw his well-struck set piece go wide of the post.
As the game entered the final quarter, Lois Maynard had a volley well saved by Glennon before Forest Green went up the other end only to see Parkin curl over from 20 yards.
With 11 minutes remaining, the visitors were handed a lifeline when Guthrie was felled by Scott McManus in the penalty area, but from the resulting spot kick, Norwood's effort was saved by Glennon.
Things went from bad to worse for Norwood after he received a straight red card and that enabled Halifax to see out the remaining minutes to move to within touching distance of the top five.