Alex Baptiste punished the hosts for failing to clear an early corner, prodding home from close range.
A miscued clearance from home keeper Tommy Lee allowed Che Adams to stroke the Blades' second into an empty net.
United's Ryan Flynn volleyed over, only for Billy Sharp to add a third against a Chesterfield side that remains four points above the relegation places.
Blackpool, who are in the last relegation spot, can move to within a point of the Spireites if they beat Rochdale later in the day.
Sheffield United eased to victory at the Proact Stadium to increase Chesterfield's relegation fears.