After a shaky start, the home side started to show the class that has earned them three consecutive wins with Luke Chadwick and John Halls linking well on the right to cause the Derby defence problems.
However, after conceding possession in a dangerous area, Phil Brown's men had their first chance of the game when Steve Simonsen had to get down quickly to save a long range Inigo Idiakez shot.
County's best chance of the half came from a set piece when after Dexter Blackstock was fouled 35 yards from goal, Spaniard Idiakez flighted a dangerous shot that flew wide of Simonsen's right post.
Stoke drew first blood after 33 minutes when Halls' throw from the right was flicked into the six yard box by Chadwick and comfortably placed into Lee Camp's bottom left by Sam Bangoura.
City were unlucky not to go further ahead in the following six minutes with two Paul Gallagher free kicks both being saved superbly by Camp.
The visitors pulled level in the 64th minute when a cross from the right by Blackstock curled in dangerously for Tommy Smith who pulled ahead of Michael Duberry to send the ball looping over a grounded Simonsen.
Only five minutes later, The Rams took the lead when an Idiakez free kick from way out on the left found Lewin Nyatanga who climbed highest to head the ball into the goalkeeper's bottom right corner.
Stoke never gave up but their efforts were in vain as the heroics of promising young goalkeeper Camp denied Bangoura twice during the last ten minutes.
The Guniean striker could have been forgiven for thinking he had scored again one minute from time when his header flew towards goal off a Halls cross but Camp's superb reactions denied any equaliser to give his side some much needed points.