Fourth-placed Bury lost 1-0 at league leaders Brentford on Saturday and suffered their first home defeat in nine as the Spireites held on after first-half goals by Aaron Downes and Jack Lester.
The hosts were handed a lifeline when Gregor Robertson was sent off in the 42nd minute and although Andy Bishop pulled one back with a 60th-minute penalty, the Spireites stood firm.
Bury were caught napping from a long throw by Dan Gray in the second minute and Downes could barely believe his luck as he stabbed the loose ball home from close range.
Downes was in more familiar territory moments later as he prevented Mike Jones getting a shot away for Bury.
Lester then pounced on a wayward pass by Bury defender Ryan Cresswell to fire into the side-netting before Lloyd Kerry should have scored in the 19th minute, the Chesterfield midfielder blazing over after being played in by Lester.
Bury twice went close to levelling from a Jones corner in the 28th minute, with visiting keeper Tommy Lee punching out a Ryan Cresswell header before Andy Morrell was unable to keep a close-range effort down.
Chesterfield's Martin Gritton then fired narrowly wide from 20 yards from Lester's lay-off while Bury's Efe Sodje had a header cleared off the line by Kerry from a Brian Barry-Murphy corner.
The Spireites then went straight up the other end to double their lead, Lester latching onto Kerry's pass and setting off on a run round two defenders before slotting past Tyler.
Robertson saw red moments later for a late challenge on Elliott Bennett, who was set to charge into the Chesterfield box.
Cresswell headed over shortly after the break, while Baker fired narrowly over before Gray was penalised for bringing down Jones and Bishop slammed home the spot-kick.
Winger Jones then fired over after neat footwork by Bishop and Morrell, before Bishop chipped onto the roof of the net with 15 minutes left and Jones spurned another great chance at the death.