The Spireites dominated the first half and had a goal disallowed for offside when Aaron Downes headed home Gregor Robertson’s free-kick.
Top scorer Jack Lester and on loan midfielder Lewis Montrose both went close while Martin Gritton should have scored when he fired over from close-range after good work from Jamie Lowry.
Rotherham took the lead six minutes before the break when Reid turned in the area to fire Micky Cummins’ cross beyond the reach of Tommy Lee.
Rotherham continued in the same vein after the break with Reid notching his 15th goal of the season after Drewe Broughton nodded Pablo Mills’ long ball into his path.
Drew Talbot was sent off for the visitors after picking up two bookings before Mills sealed the win with eight minutes remaining with a 20-yard drive.