Jacob Brown scored the only goal as Stoke recorded a 1-0 win which pushed Derby closer to the relegation zone.
The winger headed home with 16 minutes to go to make it seven games without victory for the struggling Rams.
The visitors, who are winless since February 23, failed to register a single shot on target during a lacklustre display.
Defeat leaves them just five points ahead of third-bottom Rotherham, who have four games in hand.
Stoke enjoyed the better of the first half in terms of territory and possession although the game started slowly, with Andre Wisdom and Teden Mengi clearing early Tommy Smith crosses as the home side pegged Derby back.
Visiting goalkeeper Kelle Roos made a decent save after Brown was flagged for offside from Joe Allen's pass after 14 minutes, while Smith picked up a yellow card seven minutes later after going through the back of Lee Buchanan.
Roos then spilt a Brown shot out for a corner after the Stoke man got a strike away from a tight angle in the 23rd minute.
Smith picked up a knock five minutes later following a Buchanan tackle to further hit the flow of the game.
Powell was caught offside after 36 minutes as Derby's well-organised defence continued to stifle the hosts.
Adam Davis cut out Buchanan's dangerous cross in the 39th minute before Colin Kazim-Richards drilled a long-range effort wide as Derby finished the half strongly.
Powell sent a shot wide five minutes after the interval before Sibley dragged an effort past the post soon after having found space just inside the box.
Powell skied a shot high and wide a minute later after Buchanan put him under pressure and Kazim-Richards became the latest player to miss the target after 56 minutes as the game briefly opened up.
Derby's Nathan Byrne was fortunate to escape a booking after hacking down Powell in the 68th minute, while Graeme Shinnie just failed to get on the end of Jason Knight's drilled cross a minute later as the visitors pushed for a much-needed goal.
However, it was Brown who finally broke the deadlock when he headed home from Powell's cross after 74 minutes.
Roos got down well to turn away Danny Batth's header as Stoke threatened a second before Brown hit the follow-up into the side netting.
Mengi blazed over after a corner dropped to him as Derby's last chance went begging with five minutes to go.