The Millers, without a win since the opening day of the season, were ultimately good value for the three points in a match that could have gone either way in the first half in particular.
The Millers started on the front foot and in just the second minute Ben Hutchinson played a lovely ball to Opoku in an advanced position. He was dispossessed but the ball fell to Sargent who hit a fierce drive from outside the box which was heading into the top corner until an excellent save by Burton-loanee Jack Livesey.
At the other end Kieran O’Connell whipped over a cross from the left which Martin Smyth just failed to connect with in front of goal.
Smithson was having a productive afternoon and he sped down the right, sent over a lovely cross to Opoku in the area. With his back to goal he turned delightfully but didn’t connect properly with his shot and Livesey was able to scramble the ball away for a corner.
O’Connell responded and he hit a shot which drew a comfortable save from Jack Steggles.
It was end-to-end stuff and O’Connell did get the ball in the net on 15 minutes but his close-range effort was correctly ruled out for offside.
Opoku, who caused the Moatmen problems all afternoon, was next to advance and he hit a superb cross which Hutchinson missed by inches.
Gresley should have done better on 28 minutes when Eric Graves found himself in a good position on the right hand side of goal, but he fired his shot high over the bar.
Carlton made them pay on 32 minutes with a lovely goal. Sargent, impressing in midfield, played the ball up to Opoku, just inside the area with his back to goal. He was marked tightly but he swivelled, created a yard of space and fired into the top corner from 15 yards.
The second half was a more scrappy affair as both sides cancelled each other out. Carlton were content to keep Gresley at arms-length and launch attacks by using Walker’s long throw and raids down the flanks from Smithson and Davie. Opoku hit one overhead kick over the bar while Hutchinson saw a shot comfortably saved.
Gresley failed to test Steggles at all in the second period, with the Millers defence proving too strong for the hosts.
They did have an opportunity with five minutes remaining when they broke quickly from a Carlton corner but, with two men available at the far post, the cross was misplaced and Davie was able to clear.
Carlton saw out the remainder of the match fairly comfortably to secure a valuable three points and make it two wins out of two away from home in the league.