The Canadian international finished from close range after a low cross from Morten Bisgaard had opened up Stoke's suspect defence.
Derby had gone in front in first-half injury time through Inigo Idiakez but Carl Hoefkens appeared to have rescued a point with an equaliser on the hour only for Peschisolido to shatter the visitors.
The match was open throughout with both teams finding plenty of space in and around the penalty areas.
The only surprise was that Derby did not find the net until Idiakez produced a spectacular finish from 25 yards to leave goalkeeper Steve Simonsen helpless.
Simonsen had made good saves from Mounir El Hamdaoui and Tommy Smith before that but Stoke also had their moments with Hannes Sigurdsson denied by a goalline clearance from Peter Whittingham.
Replays appeared to show that the ball had crossed the line before Whittingham cleared but Stoke did at last get some reward for their neat attacking, although there was an element of good fortune about the equaliser.
Luke Chadwick's cross from the right bounced off the back of a Derby defender and fell inviting to Hoefkens on the edge of the box and the Belgian's right-foot shot took at least one deflection before going in off the inside of the left-hand post.
Derby responded with an Idiakez free-kick that just went narrowly wide before Stoke had the best opportunity with five minutes remaining but Mamady Sidibe wastefully headed over from eight yards.
It was a bad miss and he was made to pay when Derby broke forward with Idiakez finding Bisgaard out on the right and the Dane's low cross was turned in by Peschisolido from a yard out to secure Derby's first win since August.