The Derby striker opened the scoring when his cross-shot deflected off Burnley winger Wade Elliott.
Gareth O'Connor levelled before the break when his fine 25-yard strike nestled in the bottom corner.
But Peschisolido restored the Rams' lead with 23 minutes to go when he chipped home from 15 yards for his fifth goal of the season.
Burnley had started the brighter of the two sides and the lively Ade Akinbiyi caused problems for the home side early on.
Veteran goalkeeper Kevin Poole was forced into a couple of decent saves - including a superb double stop to deny Chris McCann and Akinbiyi in quick succession.
But Derby went ahead against the run of play on 17 minutes when Peschisolido found space on the left flank and hit a low shot which was deflected into his own net by Elliott.
O'Connor deservedly dragged the visitors level within 11 minutes when he fired home a superb shot past Poole.
Akinbiyi wasted a great chance to put the Clarets ahead after half time when Elliott skipped to the byline and crossed but the big striker shot wide with the goal gaping.
Peschisolido made Burnley pay when he collected Inigo Idiakez's pass 15 yards from goal and chipped home into the far corner.
Derby: Poole, Edworthy, Nyatanga, Michael Johnson, Kenna, Smith, Thirlwell, Seth Johnson, Holmes, Peschisolido (Bolder 90), Idiakez.
Subs Not Used: Camp, Bisgaard, Doyle, Barnes.
Booked: Michael Johnson, Idiakez.
Goals: Peschisolido 18, 67.
Burnley: Jensen, Sinclair, McGreal, Duff (Thomas 87), Harley, Elliott (Branch 87), Hyde, James O'Connor, Garreth O'Connor, Akinbiyi, McCann.
Subs Not Used: Karbassiyoon, Spicer, Courtney.
Booked: Akinbiyi, Sinclair.
Goals: Garreth O'Connor 29.
Att: 12,713
Ref: M Jones (Cheshire).