Preston right-back Graham Alexander scored his first brace of goals in the first half with a superb shot after 12 minutes and then a penalty after 43 minutes.
Preston had a great chance after three minutes when home debutant Patrick Agyemang, signed from Gillingham, beat three defenders but his shot was saved by the keeper.
Chris Sedgwick, also making his home debut, fired over and Richard Cresswell had a close-range shot saved by Derby keeper Lee Camp.
In the 12th minute Eddie Lewis hit a cross and Alexander took the ball inside before dispatching a 10-yard shot into the top corner of the net to make it 1-0.
The referee awarded Preston a penalty after 43 minutes when a Lewis corner was handled by Grzegorz Rasiak.
Alexander hit the penalty to the keeper's right to make it 2-0.
In the second half Rasiak had a 10-yard header saved by Jonathan Gould from a right-wing cross.
Paul McKenna was booked for a foul on Tommy Smith in a central position after 64 minutes.
Derby manager George Burley brought on Morten Bisgaard for Blessing Kaku after 66 minutes and Smith was booked for dissent after 71 minutes.
More substitutes followed with Rasiak and Marco Reich being replaced by Paul Peschisolido and Marcus Tudgay. Omar Daley came on for Sedgwick after 75 minutes.
Cresswell scored his 12th goal of the season with a close-range flick into the net from an Agyemang right-wing cross.