Finley Munroe headed the visitors in front on eight minutes from Ollie Palmer’s cross but John Fleck equalised with his first goal for the club two minutes later.
The Blues were the better team for the rest of the first-half but they fell behind just after the hour when Joe Snowdon drilled in following a Will Wright corner.
Chesterfield huffed and puffed in the second 45 but they could not find a leveller despite Munroe being sent off with five minutes of added-time remaining after collecting his second yellow card.
The defeat is the Spireites’ first loss in 10 in all competitions and it the result means they drop out of the play-off places.
Here are our player ratings from the game...
5. Lewis Gordon 6
Comfortable outing. Up and down the left. Strong in the tackle. Replaced for the fresh legs of Lewis with 20 to go. Photo: Tina Jenner
6. John Fleck 8
Our man of the match. Outstanding at times.Thumped in an instant equaliser to make it 1-1, his first goal for the club, running off the back of former Spireite Darren Oldaker. Came close to adding what would have been a stunning long-range second moments later. Made tackles and got around second balls. Photo: Tina Jenner
7. Tom Naylor 6
Saw lots of the ball in the first-half and he helped control the play and sustain attacks. His influence softened in the second-half. Off with 20 remaining. Photo: Brian Eyre
8. Dilan Markanday 6
Assertive and direct in his attacking play in the first-half and nearly grabbed an assist. Kept quiet after the break and brought off with 13 minutes remaining. Photo: Submitted