Opoku, with his back to goal, swivelled and fired into the top corner from just inside the area shortly after the half hour to maintain Carlton's 100% away record.
In an end-to-end first half Gresley goalkeeper Jack Livesey made a stunning save from Khyle Sargent while at the other end Kieran O'Connell saw a goal ruled out for offside.
The Moatmen struggled to create chances in the second half and Carlton secured the win in relative comfort.
The Millers move up to 11th in the table with six points from four games.
Carlton return to action on Tuesday with a trip to Stocksbridge Park Steels.
A full report on today's game will be on site over the weekend.
Updated 23:15 - 8 Sep 2018 by Alan Murphy