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...
9. Ronan Darcy 6
Involved in the first-half, having plenty of touches. Another one who was always on the move and trying to find space. His influence softened after the break and he was brought off with 25 to go. Photo: Tina Jenner
10. Dylan Duffy 8
Two assists in the first 45 as he crossed low from the left for Bonis to finish before then crossing beautifully from the right for the striker to flick home. He grafted, chased everything down and pressed hard. Withdrawn with 20 to go. Photo: Tina Jenner
11. Lee Bonis 9
Two goals in the first 45. He finished at the second attempt for the opener and then his close-range flicked header doubled the lead. He could have had another but he miskicked his finish. He impressed off the ball too. Off on 70. Photo: Tina Jenner
12. Vontae Daley-Campbell 6
On for Tanton on 66 and kept things tight at the back. Photo: Brian Eyre