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...
1. Zach Hemming 6
Zach Hemming 6 Played one of the passes of the matches with some quick-thinking to spark a counter-attack. Didn't stand a chance with Ofoborh's thunderous finish. Photo: Submitted
2. Sam Curtis 5
Sam Curtis A little bit off it by his high standards, particularly in possession, and he was withdrawn on the hour. Photo: Submitted
3. Chey Dunkley 6
Chey Dunkley 6 A man-mountain the air in the first-half, getting his head on everything that came his way. Kept Tshimanga out of the box and his used his know-how to nudge him off balance when the striker was presented with a big chance before the break. Photo: Submitted
4. Sil Swinkels 6
Sil Swinkels 6 Defended his box well apart from one lapse in concentration and kept the ball neatly ticking over. Didn't take any chances as he mopped up and made one vital challenge in the box to keep Chesterfield in the game. Photo: Tina Jenner