Armando Dobra scored the winner on 82 minutes after a dominant performance which should have resulted in more goals but for some top saves from goalkeeper Mark Cousins.
The clean sheet was the Spireites’ first of the season and it helped them go top of the table.
Assistant manager Danny Webb said: “What I really enjoyed was that there was not a sense of resignation amongst the team when it looked like being a frustrating day.
“Their goalie was man of the match with 10 really good saves so it would have been ever so disappointing had we not won when we dominated from start to finish.
“You can go through all the players - including the subs - they all brought something to the table. From one to 11 it was a really good job well done.”
On the first clean sheet, he continued: “It is brilliant. Hopefully that seed of doubt from people which was there - and rightly so because we had conceded far too many goals - will disappear. It certainly is a great reward for those players because they are working so hard to keep clean sheets. Hopefully that is a turning point now.
“We defended in one shape sometimes and attacked in another. We worked on that in training. The boys knew what was asked of them. It was up to the boys to execute it and I thought they executed everything really well today and we didn’t become too one dimensional. We are top of the league for a reason. We have kept that balance between being a really attractive team and a team which can mix it up.”
Chesterfield ended the match with 10-men after Michael Jacobs received a second yellow card.
On that, Webb said: “It is disappointing really. I understand that they are clamping down on time-wasting - I totally get that. I was always under the impression that they had to warn them but it seemed to go from a throw-in, to a few people moaning, to a second booking.”