Chesterfield had the first real chance of the afternoon, when Nathan Pond's attempted clearance deflected off the legs of Eoin Doyle only for Chris Maxwell to scamper back and save any blushes for Fleetwood.
It was Chesterfield again who came close to breaking the deadlock in the 34th minute when Jay O'Shea squandered a great chance to take the lead after a Gary Roberts through-ball.
Fleetwood seemed to come out of the half-time break with more purpose but could not manage to find their way past the visitors.
Nathan Pond could have snatched victory for his team at the death when his effort missed by whiskers after a Steven Schumacher free kick.
Pond's miss became the last meaningful piece of action in a hard-fought game that saw Fleetwood's impressive 100% record come to an end.