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...
5. Gavin Gunning 9
Immense. Man of the match. Captained the team with Evans benched and he led by example. Dropped into centre-back in place of Hollis and did not miss a kick and was excellent on the ball. Looks far more at ease in defence than midfield. Played his part in the goal by bringing the ball down and setting Tyson on his way. Photo: Phil Tooley
6. Laurence Maguire 8
A very consistent performer now, proved by the fact he was the only one of the back three to keep his place in the team from Saturday's defeat. Got forward brilliantly in the second half. Photo: Dean Atkins
7. Alex Whittle 8
Very good. Joined in attacks and roamed around as if he was playing a free role. At one point he was on the right wing trying to make something happen. One shot went flying over the bar in the first half after nice build-up play. Deserves to keep his place. Photo: Dean Atkins
8. Curtis Weston 8
Excellent. Looked back to his best after an off-day against Stockport. He was particularly good in the first half with some lovely passes to find a man in space. Photo: Tina Jenner