It looked as though the visitors had been rewarded for their early pressure when Will Grigg nodded in fellow Northern Ireland international Shane Ferguson’s whipped free kick after 17 minutes, only for the linesman to flag for offside.
The Millers struggled to break down a compact Dons defence throughout the remainder of the first half, failing to register a shot on target despite dominating possession.
The hosts looked more vulnerable after the break, and the league leaders finally broke through in the 60th minute when Joshua Kayode raced onto Chiedozie Ogbene’s pass before slotting into the bottom right corner.
It looked as though the floodgates had opened when Wes Harding connected with Michael Smith’s flick-on, his looping header clipping the bar before bouncing to safety.
The hosts failed to mount a serious challenge in search of an unlikely equaliser, with Mark Robinson’s side now 12 games without a win in all competitions.
Millers boss Paul Warne said: “[It was] OK. A good away performance, kept another clean sheet, I think we've only conceded five away from home or something.
"I thought from the first kick off we were trying to win the game, trying to go after it. Draws are no good to us, we are trying to rab the game by the throat and I thought we really did. We created enough chances to win and I think we deserved it.”