The home side thought they had grabbed the lead after just two minutes when Alan Goodall headed past Tommy Lee but Antoni Sarcevic was judged to be offside.
Town bossed the opening exchanges but fell behind against the run of play when Gary Roberts' free-kick was neatly turned home by Ian Evatt.
Sam Morsy then doubled the Spireites' advantage, taking advantage of a spill by Scott Davies to rifle home from 18 yards.
Fleetwood thought they had pulled one back when Jon Parkin bundled home, Chesterfield mounting a concerted protest which eventually yielded another offside flag.
But they did grab one before the break, Conor McLaughlin feeding Parkin who flicked it neatly onto the head of David Ball.
Chesterfield restored their two-goal cushion just after the hour, Jimmy Ryan finding space 20 yards out to launch a curling effort past Davies.
Parkin almost made a game of it with a thundering blast from Junior Brown's cross, a last-gasp block denying the big striker.