Tom Whelan struck the only goal of the game on 37 minutes, hooking the ball into the net from inside the area after the visitors failed to clear Martin Smith’s free-kick.
Akwasi Asante hit the post in the first-half, while the visitors smacked the crossbar after the break.
The victory takes the Spireites up to seventh.
Here are Liam Norcliffe’s player ratings from the game...
1. Grant Smith 7
Smith did not have to make a notable save. His best moments came in the final few minutes when he did well to claim a couple of crosses and set-pieces to take the pressure off. Three clean sheets in a row for him. Photo: Dean Atkins
2. George Carline 9
My man of the match. He was at the heart of most things the Blues did in the opening 25 minutes. He won all of his duels, great in the tackle, won the ball back regularly and kept hold of it. Photo: jason chadwick
4. Haydn Hollis 8
Another solid showing. Celebrated his new contract with another clean sheet. Photo: jason chadwick