Preston had the early chances with Callum Davidson firing a 30-yard shot off target and Danny Pugh hitting a dangerous free-kick which was headed narrowly wide of his own goal by Derby striker Steve Howard.
Preston captain Graham Alexander hit a shot off target from a Pugh corner.
Ex-Preston loan player David Jones hit an innocuous free-kick straight at Carlo Nash but he juggled with the ball and it led to Michael Johnson heading against the bar and Sean St. Ledger clearing before Jon Stead had a shot cleared.
Stead had another shot off target before Preston got their best chance of the first half.
David Nugent squared the ball to Brett Ormerod who was clear but his shot was tipped away for a corner.
Howard was booked for foul on Davidson and Derby's 18-year-old midfielder Giles Barnes had a 20-yard right-foot shot which went off target.
Davidson was booked for a foul on Stead and Howard headed over with Matt Hill also shooting off target.
Dean Leacock was booked for dissent after a foul on Ormerod with Ormerod also getting booked seconds later.
Derby made it 1-0 just after the re-start when a shot by Morten Bisgaard from the right was only parried by goalkeeper Nash and Howard scored from close range.
Derby were awarded a penalty just three minutes later when Liam Chilvers, who looked outside the penalty box, fouled Stead.
Howard hit a low right-foot penalty to Nash's left and he got a touch but the ball ended up in the back of the net.
Preston pulled a goal back with ten minutes left when Nugent latched on to Alexander's cross and scored from five yards but the late surge couldn't prevent Derby taking all three points.