Goals in the first-half from Jeff King and Jake Hyde did the damage.
Kairo Mitchell bagged his first goal in a Blues shirt with 20 minutes remaining but the visitors held on.
Defeat leaves Chesterfield in the final play-off spot in seventh with nine games to go.
Town face another play-off rival in Wrexham at the Racecourse Ground on Saturday.
Here are Liam Norcliffe’s player ratings from the game...
Defeat leaves Chesterfield in the final play-off spot in seventh with nine games to go.
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James Montgomery made his debut in goal. Photo: Rachel Atkins
. James Montgomery 6
James Montgomery was handed a surprise debut with regular stopper Grant Smith dropping out in what boss James Rowe said was a tactical switch rather than down to injury. Jeff King's soft effort from the edge of the box went through a crowd of bodies, giving Montgomery little time to react, before nestling into the bottom corner. Any criticism aimed his way is a bit harsh for me. He had no chance with the second and had little to do apart from pick the ball out of his net twice. Photo: Rachel Atkins
. George Carline 6
Got forward more in the second-half than in the opening 45. Town tried to hit him on the diagonal more which they did not manage to do in the first-half. Delivered a decent cross which Tyson almost acrobatically finished. Photo: Rachel Atkins
. Fraser Kerr 6
Had a good chance to equalise deep into stoppage time but Halifax goalkeeper Sam Johnson denied him with a great save. Photo: Rachel Atkins
9. Tom Whelan 5
Looked a bit lost and was ineffective. Had one shot on target in the opening 45. Another one who Rowe did not seem happy with from the touchline. Subbed off 10 minutes after the break. Photo: Rachel Atkins
10. Liam Mandeville 6
Can't fault his effort or commitment. He wasn't in the game at times and then he would pop again. No real goal threat, though. Replaced with 10 to go. Photo: Rachel Atkins
11. Kairo Mitchell 6
Started brightly and was denied by Halifax stopper Johnson with a good, one handed save down to his left. Was isolated for most of the first-half after that. Recovered to score his first goal in a Town shirt with 20 minutes to go, pouncing on an error by Maher. Also played a nice one-two with Tyson before firing over from the edge of the box. Photo: Rachel Atkins
12. Nathan Tyson 6
Came off the bench at half-time to partner Mitchell up front. His acrobatic attempt from Carline's cross went flying over the bar. He had an impact, as he normally does. Photo: Rachel Atkins