The all important goal came six minutes before the break when Paul McMullen lashed home from close range after the Millers failed to clear a free kick at the near post.
In a fiercly competitive game, the Millers were grateful to goalkeeper Andrew Richmond for a couple of excellent saves as well as some last ditch tackles by all of the defenders who kept the home side at bay.
At the other end, Carlton struggled to create clear chances. Reuben Wiggins-Thomas came closest in the first half, but goalkeeper Matt Cohen foiled his attempt to go round him.
In the second period Carlton had to wait until the 90th minute before creating another such opportunity. This time substitute Sam McVicar had the goal in his sights, but wanted a split second too long to dispatch his shot and Matt Johnson was able to block.
The Millers need to stop the rot quickly before they slip out of the play-off positions. The next chance to do this is on Saturday when they entertain the men from the hills, New Mills.
A full report on tonight's match will appear on Thursday.