The Spireites won at Halifax.
The Spireites went ahead in the 15th minute when Liam Mandeville headed in after a long throw was not dealt with.
Mais Halifax responded just after the half hour as Darren Stephenson cut in and fired a left-footed shot home at the near post.
The hosts then went in search of another goal, with Martin Woods, Neill Byrne and Jake Hyde all off target.
Halifax somehow missed the chance to move 2-1 ahead in the 50th minute as James Montgomery saved Hyde’s header and Manny Oyeleke cleared the rebound off the line before Nathan Clarke volleyed just over.
But it was Chesterfield who netted the winner 11 minutes from time, with substitute Nathan Tyson tapping in Mandeville’s cross.