The away side went ahead on 19 minutes when Michael Cheek raced clear to finish for his 18th goal of the season.
Laurence Maguire, skippering the Blues, levelled with a well-taken finish inside the area following a corner from Tom Whelan.
But the Ravens pinched all three points at the Technique Stadium when Joe Kizzi headed in at the far post.
Here are Liam Norcliffe’s player ratings from the game...
. ndet 17-4-21 chesterfield b.JPG
Chesterfield suffered a late defeat to Bromley on Saturday. Pictured: Nathan Tyson. Photo: jason chadwick
. Grant Smith 6
Conceded two but there was not much he could have done about either of them. Apart from the goals, he had very little to do in terms of saves. His handling and distribution were good. Photo: Dean Atkins
. George Carline 7
He was at the centre of two strong penalty shouts, one in each half, the second looked stonewall. Meanwhile, his long throw was headed against the post by Kerr in the first-half and Tyson might have done better with a header from his cross in the second-half. A commited and hearty performance as always. Photo: jason chadwick
. Josef Yarney 6
With Gunning not involved, Yarney started on the right of a back three with Kerr moving in one. He fizzed a great ball into the feet of Mitchell on the edge of the area which led to a chance for Weston which was cleared off the line. He also played some other good channel balls. Perhaps went long a bit too much at times but he was aggressive and decent in the air. Photo: jason chadwick
. Fraser Kerr 6
Hit the post with a header from Carline's long throw. He also brought a good save from Bromley stopper Cousins when he headed towards goal from Whelan's corner. Bromley's first goal went straight through the middle of Town's defence so Kerr might have done better with his positioning for that one. Photo: Craig Brough/AHPIX LTD
1. Grant Smith 6
Conceded two but there was not much he could have done about either of them. Apart from the goals, he had very little to do in terms of saves. His handling and distribution were good. Photo: Dean Atkins
2. George Carline 7
He was at the centre of two strong penalty shouts, one in each half, the second looked stonewall. Meanwhile, his long throw was headed against the post by Kerr in the first-half and Tyson might have done better with a header from his cross in the second-half. A commited and hearty performance as always. Photo: jason chadwick
3. Josef Yarney 6
With Gunning not involved, Yarney started on the right of a back three with Kerr moving in one. He fizzed a great ball into the feet of Mitchell on the edge of the area which led to a chance for Weston which was cleared off the line. He also played some other good channel balls. Perhaps went long a bit too much at times but he was aggressive and decent in the air. Photo: jason chadwick
4. Fraser Kerr 6
Hit the post with a header from Carline's long throw. He also brought a good save from Bromley stopper Cousins when he headed towards goal from Whelan's corner. Bromley's first goal went straight through the middle of Town's defence so Kerr might have done better with his positioning for that one. Photo: Craig Brough/AHPIX LTD