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Luke Graham's first Stoke City goal reinforced their place in the play-off positions and deepened Derby County's gloom at Pride Park.
The Scotland defender netted with a deflected header in the second half as the Potters returned to winning ways following a late defeat at home to Middlesbrough in midweek.
Victory gave Stoke their first win away against Derby since 2007, and leaves John Eustace's side still awaiting their first home win of the season, and sitting second from bottom in the Championship table.
Stoke were indebted to goalkeeper Viktor Johansson as he produced a terrific save from David Ozoh late in the game to keep the lead intact.
That late loss to in-form Boro had been Stoke's first reverse in seven games, but they had to dig deep to eke out a result in a poor game against an injury-hit Derby side who have no wins in their past six in the Championship.
The only excitement of the first half came as Rams' striker Carlton Morris threatened to burst through on goal but went down under a challenge from Bosun Lawal, bringing loud protests from Eustace on the sidelines.
Potters boss Mark Robins sent on George Hirst as a substitute at half-time but it was another Scottish summer signing who made the breakthrough just four minutes after the re-start.
Ethan Galbraith lifted a free-kick into the box and Graham, signed from Dundee, saw his header strike Morris on the back and loop beyond the grasp of Rams keeper Josh Vickers.
With Lewis Travis limping off shortly afterwards, after making his first start since August due to injury, Derby were cursing their luck.
They offered a response as Rhian Brewster's shot glanced off the outside of a post, but Stoke countered dangerously, with Hirst, Djibril Soumare and Justin Devenny all going close to adding a second.
Derby summoned one last effort and almost snatched a point as Morris headed the ball on and Ozoh's volley was heading for the bottom corner until Johansson got down brilliantly to turn it away.
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