The Canadian international scored twice as he made his first start since late October to punish the visitors for wasteful finishing.
Burnley were undoubtedly the better side for long periods but Ade Akinbiyi had an awful afternoon and was guilty of three glaring misses while centre-half John McGreal put four unmarked headers wide.
Peschisolido had two openings and put them both away, although the first needed a big deflection to beat Brian Jensen.
But their was nothing fortuitous about his 67th minute winner which came when he chipped the big goalkeeper from the right side of the penalty box after Inigo Idiakez had set him up.
Burnley had drawn level through a long-range effort from Garreth O'Connor but in the end Peschisolido was the difference between the teams.
Certainly Burnley would have won the game if Akinbiyi had been at his sharpest as the visitors sliced Derby open time and time again.
It was almost too easy for their midfield as they exposed glaring weaknesses but the end product was missing.
Only Akinbiyi will know how he failed to put the ball in the net in the 17th minute after Kevin Poole had beaten out a shot from Chris McCann.
But Akinbiyi hesitated and allowed Poole to block his shot and minutes later he again failed to react quickly enough and Michael Johnson put the ball out for a corner.
By then, Peschisolido had given Derby an 18th minute lead when his shot looped off Wade Elliott and sailed over Jensen and inside his left-hand post.
Burnley got the reward for their superiority when O'Connor picked up the ball and drove a right-foot shot past Poole from 25 yards but they could not build on that.
Akinbiyi's afternoon went from bad to worse in the 59th minute when he sliced horribly wide from four yards leaving Peschisolido to grab the winner in the 67th minute.
Idiakez broke away and when his pass picked out the Canadian his deft chip was measured to perfection leaving Jensen helpless for a second time.