Rhoads broke clear of the Millers defence and fired past Jack Steggles to end Carlton's 100% away record.
The Millers had been the better side in the first half, enjoying a lot of possession and putting the hosts under pressure with Aaron Opoku, Ben Hutchinson and Luke Smithson all having chances to score.
Carlton changed their formation early in the second half and this seemed to hand the initiative to Steels, who saw Steggles make a couple of excellent saves to prevent them scoring.
Hutchinson thought he had scored when his low drive seemed to cross the line before it was cleared but the linesman said no goal.
With Steels pushing forward Rhoads ran onto a Tyler Williams pass to secure the win.
There was further misery for Carlton when Riece Bertram was sent off in added time for a second yellow card.
A full report will be on site tomorrow.
The Millers return to action on Saturday when they entertain Frickley Athletic at Stoke Lane.
Updated 23:58 - 11 Sep 2018 by Alan Murphy