Earlier in the week, Dennis Wise had failed with a request to have Miller replaced and the Leeds manager's misgivings seemed to be confirmed after only nine minutes.
The Durham official penalised Leeds midfielder David Prutton for a mild challenge on Jason Demetriou near the left touchline and Sean Thornton floated a free-kick into the far top corner as keeper Casper Ankergren misjudged the flight of the ball.
It was only the second goal Leeds had conceded in nine league and cup matches and the first time they had been behind in a league game since the opening match of the season.
Leeds fans reacted by chanting '1-0 to the referee', but Miller silenced them in the 32nd minute by showing Thornton a red card for a challenge which left Frenchman Seb Carole needing treatment to the side of his head.
Moments earlier, Thornton had fired a shot against the far post but a flag was raised for offside.
Leeds almost equalised just before half-time when Carole's header was cleared off the line by Tamika Mkandawire.
But Carole was celebrating ten minutes into the second half when he took a short corner to Alan Thompson, accepted a return pass and fired a left-foot shot past Stuart Nelson from just inside the penalty box for his second goal of the season.
Leeds were awarded a penalty in the 82nd minute when Paul Terry brought down Carole, but Tresor Kandol spooned the kick high over the bar.
Then on 86 minutes, Adam Boyd thought he had scored when his shot squirmed through Ankergren's hands and seemed to cross the line before the keeper recovered but play was waved on.