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...
1. 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
2. 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
3. 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
4. Gavin Gunning 6
Returned to the starting line-up after missing out against Bromley. A great tackle towards the end stopped Halifax adding a third on the counter. Good to see him back and hopefully he can stay clear of injuries. Photo: Craig Brough/AHPIX LTD