The Spireites started brightly and Liam Mandeville should have scored after 90 seconds but he fired into the side-netting. The visitors continued to control play and created a couple of other half chances. But the hosts finished the first 45 strong with Danny Collinge volleying against the crossbar and then Kabongo Tshimanga wasted a good chance.
The Bees had the better of the play after the break and a well-worked move was blasted into the top corner by Nnamdi Ofoborh on 65 minutes.
Armando Dobra had a shot cleared off the line and Mandeville volleyed over from close-range but the Blues, who were off the pace in the second-half overall in a match they were once again not ruthless enough in, fell to their first defeat in seven at The Hive on Saturday.
Here are our player ratings from the game...
9. Liam Mandeville 5
Liam Mandeville Had a big chance after 90 seconds but he lashed into the side-netting from inside the box, which he might be disappointed with, and he might feel he should have done better with a header later on. And he wasted another good chance when he volleyed over from close-range in the second-half. He was withdrawn moments later. Photo: Submitted
10. Dylan Duffy 5
Dylan Duffy. Reasonably quiet from an attacking perspective as he let Pearce run beyond him. Lashed one shot wide inside the area. Taken off on the hour. Photo: Brian Eyre
11. Lee Bonis 5
Lee Bonis Had a half chance with a header early on but it glanced wide. Ran the channels and tried to hold it up, with varying success. Scrappy outing. Off on 60. Photo: Submitted
12. Will Grigg 6
Will Grigg Replaced Bonis on 60. Gave Town more of a focal point. Photo: Tina Jenner