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...
1. Zach Hemming 7
Made a key save at 2-1 early in the second-half as he spread himself big to block from Stead. Showed a safe pair of hands to hold Ofoborgh's testing drive from distance. Photo: Leila Coker
2. Devan Tanton 7
A good outlet early doors as Chesterfield started on the front-foot. Had his hands full with a tricky customer in Kanu but he stood up to the challenge. After a run of games his legs were saved on 66 minutes as he was replaced by Daley-Campbell. Photo: Submitted
3. Kyle McFadzean 7
Batted everything that came his way back towards Barnet in a no-nonsense display. Blocked Stead's shot with his arm but it was hit at him from close-range so it might have been harsh had that been given. Put his body on the line in the second 45. And he had another shot! Photo: Submitted
4. Chey Dunkley 7
Aggressive in his defensive headers as he attacked the ball with plenty of venom and you could hear his bellowing orders. Mopped up and read things well at the back in the second 45. Photo: Submitted