Kidsgrove had the better of the first half and perhaps should have scored long before they did - the opener coming 5 minutes before half-time from Kingsley Adu Gyamfi.
Chasetown's closest attempt was a curling Levi Reid effort wide of the upright.
The Scholars started the second half brightly - a couple of whipped in crosses eluded strikers in the six yard box and then a strong penalty appeal was turned down for what looked like a foul on Liam Kirton.
The hosts went straight up the other end and made it 2-0 through Lee Williamson with 19 minutes remaining.
A late Williamson penalty (86) and a goal from Oliver Jepson (88) gave the final scoreline a very one-sided feel.