The visitors started brightly but the Spireites dominated most of the game and got their reward in the end.
Akwasi Asante finished low inside the area after substitute Nathan Tyson, making his first appearance in four months, picked him out.
Eastleigh thought they had taken the lead with 15 minutes to go through Danny Hollands but it was ruled out for offside.
Here are Liam Norcliffe’s ratings out of 10...
9. Martin Smith 8
His first league start for Town. Really grew into the game. Started to get on the ball more from around 25 minutes onwards and showed his quality. Replaced by McCourt with 20 minutes to go. Photo: Phil Tooley
10. Tom Whelan 8
Back in the starting line-up after a three-match suspension and he provided Town with some much-needed energy and pressing further up the field. He played in advanced role just behind Asante. Had a good chance to score in the first half but fired wide inside the area. Great to see him back. Replaced by Tyson with 12 to go. Photo: Tina Jenner
11. Jack Clarke 7
Another one who grew into the game on his first start since joining on loan from Aston Villa. He was up and down in the first half but showed a lot of quality and desire after the break. Was unlucky not to score or grab an assist himself in the second 45. Photo: Tina Jenner
12. Akwasi Asante 8
You wondered if it was going to be one of those nights but then Asante made himself the hero again by slotting in with five minutes to go. He had a couple of other chances in the second half. Nine goals in 13 league games since joining. Others need to start helping him. Photo: Tina Jenner