Lee Bonis scored twice in a dominant first-half for the Spireites but Mark Shelton headed one back from a corner to get the Bees, who were unbeaten in six in the league, back into it before the break.
Town came under pressure in the second 45, Zach Hemming saving well from Callum Stead and then Kane Smith hit the post, but Liam Mandeville gave the hosts some breathing space as he added a third with 10 minutes remaining.
The victory moves the Blues back into the play-offs and into seventh.
Here are our player ratings from the game...
13. James Berry 6
Replaced Darcy on 66. Played a little part in the third goal. Photo: Brian Eyre
14. Luke Butterfield 6
On for Duffy on 70. More league minutes for him. Photo: Tina Jenner
15. Will Grigg 7
Replaced Bonis with 20 minutes remaining and he assisted the third, teeing up Mandeville with a little backheel on the edge of the box. And he nearly got on the scoresheet himself but he was brilliantly denied by the fingertips of Slicker. Photo: Tina Jenner
