Jacob Brown's fourth goal of the season, deep into the second half, was enough for Stoke to beat Derby in an uninspiring game in the Potteries.
Danny Batth almost sealed the points for the home side with another header but it was well saved by Derby goalkeeper Kelle Roos before Brown shot into the side-netting.
Louie Sibley had Derby's best moment but shot wide at the start of the second half.
It was a seventh match without victory for Wayne Rooney's Rams, who are five points above the relegation zone with eight matches remaining.
It means a nervy end to the season may now await despite having previously made good progress under the former England skipper.