The Scotland defender headed in a free-kick early in the second half and that was enough to settle a scrappy contest.

Derby, who are missing a number of key players, battled away and nearly snatched a point when David Ozoh’s shot was superbly saved by goalkeeper Viktor Johansson.

The win keeps Stoke in the top eight and leaves Derby in the bottom three still searching for a first home win of an increasingly difficult season.

Stoke had the first chance of a sunny but chilly afternoon when Lamine Cisse broke forward and pulled the ball to Jack McGlynn but his low shot lacked the power to trouble Josh Vickers.

Carlton Morris looked to have got away from Bosun Lawal who appeared to trip the Derby striker but referee Oliver Langford waved away protests.

The game became increasingly scrappy but the Rams ended the first half with a corner that fell to Sammie Szmodics but his goalbound shot was blocked by a defender.

Stoke had failed to build on a promising start and had been guilty of giving the ball away, so boss Mark Robins would have been expecting a big improvement in the second half.

His players responded by taking the lead in the 49th minute through Graham who met Ethan Galbraith’s free-kick with a header that Vickers got a hand to but the ball went in off his left post.

Derby responded with Ozoh getting the better of Lawal but he hesitated and his shot was blocked.

They had another chance in the 63rd minute when Rhian Brewster shot narrowly wide from the edge of the area and for the first time in the match, Derby were putting Stoke under pressure.

But the visitors almost got a second on the break in the 84th minute with Ben Johnson sliding a pass across to Justin Devenny who could not get a strong enough contact on his shot.

It nearly proved costly because Derby were denied an equaliser by a brilliant save from Johansson who plunged to his right to keep out Ozoh’s low drive in the 89th minute.