Nathan Ellington coolly rolled home an injury-time penalty to send Derby into the Carling Cup semi-finals.
Derby had survived everything that Stoke - and Rory Delap - could throw at them, and fought back to hit the post through Miles Addison in the second period.
The game looked to be heading for extra-time when Andy Griffin was judged to have handled in the box, and Ellington sent Derby's fans wild with the spot-kick decider.
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