Lewis Baker's piledriver was enough to maintain Stoke's undefeated start under new boss Steven Schumacher with victory at bottom side Rotherham.
The Potters midfielder crashed home a free-kick deep into first-half injury time to make it five games unbeaten since Schumacher succeeded Alex Neil last month.
Rotherham, who remain bottom of the table, made changes after the interval but rarely threatened an equaliser.
The Millers are now eight points adrift of safety, while Schumacher's side climb two places to 17th.
There were few chances for either side in the early stages, although former Stoke midfielder Sam Clucas went close for the Millers with a long-range drive that fizzed just wide of the post.