The Cuckoos opened the scoring with a penalty from Liam Hook after Toby Moore was penalised for a push.
Carlton threatened little in the opening period but were level three minutes after the break when Aaron Opoku fired home after a run and cross from Niall Davie.
Three minutes later the Millers were ahead when Moore scored from close range after a corner wasn't cleared.
The visitors had to play the final 20 minutes with 10 men after James Matthews was sent off for a high challenge, but they saw the game out comfortably and secured the win with a fine angled finish from Tyler Blake two minutes from time.
Carlton are now second in the table with 16 points from 6 matches.
A full match report will be on site tomorrow.
The Millers return to action on Tuesday when they travel to Halesowen Town (7.45pm).