Jacob Brown stole in at the back-post to head past Kelle Roos and put pressure on Derby
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.
There was almost nothing to trouble either goalkeeper until Nick Powell's cross to the far post saw Brown's run beat Jason Knight to head home.
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.
They were starved of possession and failed to record a single shot on target, even Rooney's triple substitution with half an hour remaining failed to deliver any inspiration.
Stoke also lacked quality in front of goal and only created one moment from almost 70% of the ball in the first half.
But they found a winner through Powell's delivery that was well met by Brown, who got in front of Derby defender Knight and left Roos no chance with his header.
Stoke remain 10 points off the play-off places with a mid-table finish most likely.
Stoke City manager Michael O'Neill told BBC Radio Stoke:
"We haven't had enough 1-0 wins so it's nice to get one.
"We played well in the first half but just didn't create enough opportunities and didn't get enough good balls into the box.
"Finally we got a good ball into the box from Nick Powell and a great finish from Jacob Brown after a difficult period for him."
Derby County manager Wayne Rooney told BBC Radio Derby:
"We're not on a great run of form but now we have the chance to go away and get a break mentally.
"For me it's a chance to look back on the last few weeks and reassess how we move forward.
"The players before the game didn't believe we were in a relegation battle, but now I think we clearly are."
