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...
15. Nathan Tyson 8
Came on with 12 minutes to go and had a massive impact on the game. He constantly ran in behind the Eastleigh defence and assisted Asante for the winner. It was his first appearance for four months due to injury. Photo: Steve Flynn/AHPIX LTD
4 / 4