The Millers were given the lead when Thomas-Moore, the son of ex-boss Ronnie Moore, finished from close range.
Danny Harrison then struck from distance left footed before Thomas-Moore found the top corner and Ryan Taylor thumped in the fourth from inside the box on the angle.
Thomas-Moore got his third from the spot as Patrick Kanyuka saw red for a second booking, before sub Jason Taylor completed the rout with a thunderbolt from 25 yards.
BBC Sport