Chasetown made a good start and forced the visitors into conceding fouls that resulted in two early yellow cards. From the latter, a free kick was just over the crossbar.
Liam Kirton forced an early save from visiting keeper Jack Steggles
The Millers were gifted a chance in the 25th minute after a misplaced pass from goalkeeper Curtis Pond but the keeper redeemed himself saving from Niall Davie.
Chasetown had a strong penalty claim turned down just after the half hour when Kirton appeared to be fouled by Tom Maddison.
Carlton Town took control and twice Aaron Opoku fired wide in glorious areas inside the penalty box.
After a sustained period of pressure, Carlton took the lead with a free header from Martin Ball.
Chasetown were a whisker away from an equaliser. Teenage sub Lucas Burnett fired a shot goalwards which took a slight deflection off a defender and only just eluded the onrushing George Cater from what would have been a tap in.
Steggles held a low shot from Alex Curtis, clutching to the ball at the second attempt as Kirton and Burnett waited to pounce.
Carlton broke quickly in the 87th minute and Oliver Clarke burst into the box and Tyler Johal side footed home at the near post.