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...
4 / 4