Phil Gilchrist's first goal of the season gave the struggling visitors an unexpected lead as he headed home after just four minutes.
But within 10 minutes Burnley were ahead as first Tony Grant's shot then Frank Sinclair's header made it 2-1.
The home side continued to press, but Burnley keeper Brian Jensen denied Gilchrist a last-gasp equaliser.
Rotherham caretaker boss Alan Knill:
"When your luck is out it is out and we are finding that to be the case at the moment.
"The positive is the fact that the players kept going and showed a great attitude and I know that if we carry on like that then our luck will turn.
"How we came away from the game with nothing is a mystery for we were comfortably the better side."
Burnley: Jensen, Sinclair, McGreal, Cahill, Camara, Grant, Hyde, Oster, Whittingham (Branch 70), Valois (Moore 79), Bowditch (Roche 84).
Subs Not Used: Coyne, Duff.
Goals: Grant 11, Sinclair 14.
Rotherham: Pollitt, Scott, Gilchrist, Barker, Hurst, Griffit (Keane 45), McLaren, Vernazza, Campbell-Ryce, Warne, Hoskins (Mullin 69).
Subs Not Used: Montgomery, Newsham, Minto.
Goals: Gilchrist 4.
Ref: P Robinson (E Yorkshire).