The Rams have now gone seven games without a win and have not kept a clean sheet for 11 matches.
Preston striker Ricardo Fuller was dangerous throughout the match and his 11th minute header was well saved by the England Under-21 keeper Lee Grant.
Fuller was brought down inside the penalty area after 21 minutes by Steve Elliott and Graham Alexander sent Grant the wrong way from the resulting spot-kick.
Fuller then hit the post in the 33rd minute with a ten-yard shot and a minute later loanee striker Daniele Dichio was booked for a foul on Preston captain Chris Lucketti.
Derby hit back and Elliott's 15-yard shot was brilliantly saved by Jonathan Gould who pushed the ball around the right-hand post for a corner.
Derby started the second half well and Elliott had an acrobatic 12-yard overhead kick saved by former Scotland goalkeeper Gould a minute into the second half.
Adam Bolder had a 15-yard effort saved by Gould in the 52nd minute but Preston doubled their lead 15 minutes later when David Healy played a one-two with Fuller before firing home.
Fuller scored the third goal in the 72nd minute when he turned substitute Eddie Lewis' cross home from eight yards.