French striker Vincent Pericard helped Stoke to their first home win of the season at the expense of Derby.
Peter Sweeney played a one-two with Pericard, who latched on to the return and struck home from point-blank range under heavy pressure.
City's second came when Pericard's shot from 18 yards was parried into the turf by keeper Lee Grant and Darel Russell was on hand to head in.
Derby's Ryan Smith came close but his shot was tipped over by Steve Simonsen.
Stoke boss Tony Pulis:
"It was a smashing crowd, a good game and a good tempo. Derby are a good side and I really enjoyed it.
"We created some good chances, Vincent Pericard looked a threat, Mamady Sidibe worked his socks off all night and there were spells when we played well.
"At times we gave the ball away too cheaply. Against the better sides that will hurt you."
Derby boss Billy Davies:
"You have got to defend the goal better, it's all about keeping clean sheets.
"We had chances in the first half, scraps in front of goal, but when you come here you need eight or nine of your players to be at their best
"We came for a test and, unfortunately, we failed in that test. We had too many five out of 10s."
Stoke: Simonsen, Hoefkens, Duberry, Hill (Sigurdsson 84), Higginbotham (Dickinson 69), Chadwick (Paterson 65), Russell, Brammer, Sweeney, Pericard, Sidibe.
Subs Not Used: Pulis, Duggan.
Goals: Pericard 18, Russell 58.
Derby: Grant, Michael Johnson, Nyatanga, Moore, Edworthy, Ryan Smith (Bisgaard 61), Seth Johnson (Peschisolido 60), Oakley (Idiakez 71), Barnes, Tommy Smith, Howard.
Subs Not Used: Bolder, Jackson.
Booked: Peschisolido, Howard, Moore.
Ref: M Clattenburg (Co Durham).