This was a vital match for both teams, but it was decided before the interval when City scored three times to leave Chesterfield fighting for their pride.
The Spireites did manage to salvage some of that with a much better performance, but Wayne Allison's 59th minute reply was not enough to spark a recovery.
Chesterfield will look back on two goals which came from set pieces that they failed to deal with.
City's eighth minute opener stemmed from a corner, played short to Lee Johnson who knocked it deep to the back post where Andy Smith played it back across for Richard Keogh to volley past Barry Roche from ten yards.
If Chesterfield were disappointed with the way they defended against the opener, there will also be question marks over the second which came from another corner.
This time the ball was headed out only as far as Johnson on the edge of the area and the midfielder drove a low right-foot shot into the bottom corner to put his team well on the way to victory.
Chesterfield's passing let them down far too often and City hit them again just before the break with a classic counter attack.
Cole Skuse sent Brian Wilson away down the City left and, although his shot was brilliantly parried by Roche, the ball fell to Kevin Betsy who teed it up for David Noble to sweep into the roof of the net.
Chesterfield were booed from the field but they came out with a point to prove in the second half and certainly gave their fans a much better performance.
Roy McFarland switched his formation to mirror City's 3-5-2 and the introduction of young Jamie Jackson gave his side much more spark in the final third.
For the first time, City had some defending to do and Chesterfield got a goal back in the 59th minute when a free-kick was headed across goal for Allison to drive the ball into the roof of the net from the edge of six-yard area.
Chesterfield kept plugging away but City defended strongly and almost scored a fourth goal on the break when substitute Enoch Showunmi struck the side-netting late on.