A penalty from former Derby defender Danny Higginbotham punished a needless handball by Dean Leacock and a close-range header from Dominic Matteo gave Stoke an advantage they rarely looked like squandering.
Derby huffed and puffed without ever really looking capable of getting back in the game and Stoke thoroughly deserved to revive their own play-off challenge.
Manager Tony Pulis put out a side that was designed to suffocate Derby's attacking instincts and his plan worked perfectly as the home side struggled to open up a strong defence.
At the other end, Derby's back four looked less secure and Leacock was fortunate to escape with a yellow card when he pulled back Mamady Sidibe in the ninth minute.
The centre-half was at fault five minutes later when he clearly blocked the flight of a corner with his hand and Higginbotham placed the penalty into the left-hand corner beyond Stephen Bywater's desperate dive.
Leacock was replaced two minutes later with Marc Edworthy moving to central defence and he was also booked for a late challenge on Lee Hendrie shortly before Stoke increased their lead.
A Hendrie corner drifted across the six-yard box and Matteo was allowed to place a header beyond the unprotected Bywater for a simple goal.
The damage could have been worse for the home side as Darel Russell should have scored in the 45th minute when he was through on goal, but Derby at least ended a poor first half on a bright note when Matty Oakley had a shot deflected wide.
Derby could not be faulted for effort after the break, but too much of their play was predictable and Stoke's defence dealt with everything that was thrown at them.
Steve Howard headed straight at the keeper when Gary Teale crossed from the right and the striker had another effort charged down late on.
In between those half-chances, Derby thought they had scored when Arturo Lupoli appeared to come from behind his marker to score with a right-foot shot but the flag had already gone up for an offside.
Derby were furious and their frustrations continued to build as Stoke moved closer to an impressive victory.
Russell was booked for a blatant dive near the end, but that could not detract from an excellent night's work by the visitors, whose victory will have been celebrated by Derby's promotion rivals.