Joe Snowdon hit the winner just after the hour after Spireites had battled back to go in 1-1 at half-time.
Spireites are now ninth in the table having won just won of their last six matches.
Chesterfield face a tricky away day at Cambrige in their next League Two game on December 9.
Photographers Brian Eyre and Tina Jenner took these pictures of some of the fans who were there yesterday. Take a look and see who you know.
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1. Spireites 1 Swindon 2
Chesterfield lost more ground after a 2-1 defeat to Swindon ended their previous unbeaten home league record. Photo: Brian Eyre
2. Spireites 1 Swindon 2
Chesterfield lost more ground after a 2-1 defeat to Swindon ended their previous unbeaten home league record. Photo: Brian Eyre
3. Spireites 1 Swindon 2
Chesterfield lost more ground after a 2-1 defeat to Swindon ended their previous unbeaten home league record. Photo: Brian Eyre
4. Spireites 1 Swindon 2
Chesterfield lost more ground after a 2-1 defeat to Swindon ended their previous unbeaten home league record. Photo: Brian Eyre