The League Two side took the lead after nine minutes when winger Ben Pringle planted a superb 25-yard strike into the top corner.
Rotherham doubled their advantage against their sluggish hosts after 22 minutes when a Pringle corner wasn't dealt with and Mark Bradley swept the ball home.
It went from bad to worse for County on the half hour when defender Damion Stewart was adjudged by referee Darren Deadman to have deliberately elbowed Alex Revell and was handed a straight red card.
It was 3-0 in the 41st minute as Lee Frecklington broke away from the County backline and rounded keeper Liam Mitchell before putting the ball on a plate for Daniel Nardiello to finish.
A half-time triple substitution did little to liven the home side up and Nardiello missed a glorious chance to extend the away side's lead but the three first-half strikes proved to be enough.