First-half goals from Morten Bisgaard and Inigo Idiakez were enough to secure the points and Cameron Jerome's late reply gave the scoreline a misleading look.
Derby could and should have won by a bigger margin but last season's top scorer Grzegorz Rasiak was well off the pace and Tommy Smith also wasted a great opportunity.
But Cardiff had the bigger problems on the evidence of this worrying performance.
They were frail in defence and the midfield was second best by a long way.
Perhaps it might have been a different story if Jerome had scored in the 10th minute when Derby's defence went missing.
Neal Ardley delivered an accurate cross from the right and Jerome was unmarked six yards out but he completely missed his header.
That was a big let-off for Derby who finally sparked into life when Smith drove the ball in from the left and Neil Cox was close to heading into his own net.
Cardiff were starting to struggle with Derby's quick attacks and it was no surprise when Bisgaard gave the home side the lead with an outstanding goal in the 21st minute.
He played the ball through the legs of Jermaine Darlington down by the right touchline and then beat Neil Alexander with a well placed shot into the left corner.
Smith should have scored a second when Alexander played a back pass straight to his feet but he ran the ball out of play and Rasiak then dragged a shot wide as Cardiff were opened up again.
But a second goal looked inevitable and it arrived when Darlington was forced to bring down Smith after Chris Barker had needlessly lost the ball inside the penalty area.
Idiakez put his spot-kick into the top left-hand corner and that was the end of Cardiff.
The second half was memorable only for a flurry of yellow cards as referee Trevor Kettle booked 10 players in a game that was never overly physical.
Jerome pulled a goal back after Alan Lee had headed on a corner but it was too late to change the course of a match which had long slipped away from the Welsh club.