In a tight encounter with very few chances, the hosts edged it through strikes from James Jennings and Alex Reid.
It has still been a fairly good week for Town who have collected six points from a possible nine after coming out of isolation.
The loss leaves the Spireites in 16th in the National League table, seven points off the play-offs.
Here are Liam Norcliffe’s player ratings from the game...
The loss leaves the Spireites in 16th in the National League table, seven points off the play-offs.
4 / 4