The winner came after 27 minutes, Alex Whittle firing in at the back post after Aldershot ‘keeper Mitch Walker failed to deal with Jack Clarke’s cross.
The Blues had to dig deep after the break as the hosts pushed for an equaliser but they could not find a way through a resolute away defence.
Here are Liam Norcliffe’s player ratings from the game as the Spireites moved closer to the top seven...
1. Grant Smith 7
Town protected him well but he did make a good reaction save just before half-time from Josh Rees. Back-to-back clean sheets. Photo: Dean Atkins
2. George Carline 7
Steady and solid. Joined in attacks in the first-half, defensively sound after the break. Photo: Dean Atkins
3. Fraser Kerr 8
Won all his headers and didn't put a foot wrong. Came under a lot of pressure at times but dealt with everything well. Photo: Tina Jenner
4. Haydn Hollis 9
Man of the match. A rock. Headed everything and provided a threat at the other end from Carline's long throws. He misjudged one header late on but Ricky Miller failed to take advantage. Hollis deserved a bit of luck because he was outstanding. Photo: Dean Atkins