Josh Rae had given the Millers the lead on 29 minutes but Kudakwashe Muskwe levelled just four minutes later.
Joe Lumsden put Steels ahead six minutes after the restart and that was the end of the scoring.
Another defeat for the Millers sees Wayne Scott's side sit 18th in the table with just five points from the opening seven games.
Carlton entertain Witton Albion next Saturday in their next fixture.