The visitors opened the scoring but the Millers were 3-1 ahead by half time through goals from Niall Hylton, Martin Ball and Brad Wells.
Carlton had to wait until 86 minutes before they scored again but a hatrick in three minutes from Luis Parkes sealed the win as he scored with a header, a tap-in and a penalty.
Carlton's next game is against Dunkirk on Wednesday 27 July (7.45pm).