The Spireites took all three points from Highbury Stadium on Saturday afternoon following an emphatic performance in a game that was not short of opportunity.
It was a high-tempo start to the game where both sides pressed but neither could find a way through.
A Richard Brindley long ball caught the Fleetwood defence off guard and found Marc Richards inside the area with just the keeper to beat, the Spireites striker fired low but Scott Davies was equal to it.
Moments later, a fierce Brindley cross was punched out of play by the Cod Army goalkeeper. The resulting corner was headed inches over the Fleetwood bar by Liam Cooper after Conor Townsend's cross found him on the edge of the six-yard box.
Fleetwood responded well to early Spireites pressure and forced Tommy Lee into a number of smart saves. Ryan Crowther curled an effort from the angle of the area that looked goal-bound, but Lee got across his goal to parry the ball and followed up by smothering a second attempt from a matter of yards away.
The Cod Army continued to press but could not find a way past the Spireites 'keeper who was in inspired form.
After 34' minutes, Brindley was taken off for Armand Gnanduillet as the full-back was struggling with mobility. It took just ten minutes for the French striker to have an impact and give Chesterfield the lead.
Townsend swung a corner deep into the Fleetwood penalty area where Neal Trotman returned the ball back across the face of goal into the path of Gnanduillet. The striker made no mistake in heading the ball past Davies and breaking the deadlock.
Chesterfield doubled their lead almost instantly through a fantastic goal from Richards. Trotman played a long ball from just inside the Spireites half to Gnanduillet who knocked the ball down with his chest for Richards to then hammer into the Fleetwood goal on the half-volley.
Five minutes into the second half, Fleetwood nearly found a way back into the game through Jamille Matt. The Cod Army striker pounced on weak return header from Cooper to Lee but saw his lobbed effort fall inches wide.
Richards got his second of the game and Chesterfield's third after Jay O'Shea broke clear in midfield and played a neat through-ball to Sam Togwell. The midfielder's effort on goal was deflected by Davies to the edge of the area where Richards had time to compose himself and finish high into the Fleetwood goal.
Fleetwood pulled a goal back in the 68th minute through substitute, Andrew Mangan. The Fleetwood striker's well-timed run beat the Chesterfield offside trap and left him one-on-one with Lee, Mangan then finished through the legs of the Spireites keeper.
Mangan had an opportunity to get a second as the half progressed, he brought down a lofted through-ball with his chest and advanced into the area but could only fire over.
Chesterfield defended well for the remainder of the second half and saw the game out without being substantially tested.
Fleetwood Town: Davies, Beeley, Matt (Mangan 53'), Brown, Goodall, McGuire, Crowther, Ball, Edwards, Evans (Fontaine 81'), McKenna.
Unused subs: Barry, Pond, Nicolson, McLaughlin, Lucas.
Goals: Mangan 68'
Chesterfield: Lee, Brindley (Gnaduillet 34'), Cooper, Trotman, Townsend; Togwell, Randall (Hird 73'), Darikwa, O'Shea (Henshall 84'), Talbot, Richards.
Unused subs: Whitaker, O'Donnell, Clay, Boden.
Goals: Gnanduillet 44', Richards 45', 63'.
Referee: Mr Andy Davies