Goals from Adi Yussuf, George Carline, Danny Rowe and Josef Yarney sealed the points for James Rowe’s men.
The hosts equalised on the night through Sonny Carey but the Spireites responded well and led 2-1 at the break before adding two more in the second-half.
Victory moves the Blues up to sixth with three matches remaining.
Here are Liam Norcliffe’s player ratings from the game...
1. James Montgomery 7
He did not have much to do apart from tip over Carey's free-kick in the first-half. His starting position was good. What is very noticeable behind closed doors is how vocal he is. He is always talking to his defence and organising. Photo: Rachel Atkins
2. Josef Yarney 7
With Kerr out injured, Yarney took his place on the right of a back three. After a slow start he really grew into the game and put in a good display. He capped it off by smashing the ball in for Chesterfields third goal on the night and his his first of the season. Almost got a second from Gunning's cross. A much-improved performance. Photo: Craig Brough/AHPIX LTD
3. Gavin Gunning 7
It was a big boost to see his name on the teamsheet after being a doubt with a groin injury. He was his usual commanding and vocal self. Photo: Craig Brough/AHPIX LTD
4. Laurence Maguire 7
He went close to scoring in the first-half with a long-range effort which was not far off. His header back across goal from Clarke's corner created Yarney's goal. He also produced a great block to deny Gash from 12 yards out. He played well. Photo: Dean Atkins