James Berry scored his first goal in two months when he blasted in off the post on 62 minutes after Lee Bonis forced a mistake from home goalkeeper Wyll Stanway and that turned out to be the winner in Cumbria.
The results means the Spireites, who stay seventh in League Two, have won all of their last three matches and kept clean sheets in all of them.
Here are our player ratings from the game...
1. Ryan Boot 7
Ryan Boot 7 His third clean sheet in a row and he showed more good form when he stopped Rose in his tracks as he tried to go around him when it was 0-0. Photo: Tina Jenner
2. Sam Curtis 6
Sam Curtis 6 Recalled to the starting line-up. Booked early doors. One short back pass put Chesterfield in trouble. Got forward. Replaced by Donacien for the last 20. Photo: Brian Eyre
3. Kyle McFadzean 6
Kyle McFadzean 6 Saw lots of the ball, probably having the most touches in the first-half. Booked before the break for chopping down Newby. Did what he had to do. Photo: Tina Jenner
4. Sil Swinkels 6
Sil Swinkels 6 Went about his work with no fuss and got the job done. Missed a sitter of a header which would have made it 0-2 with 15 to go. Photo: Tina Jenner