Peter Thorne took advantage of a shambolic attempt to clear a long throw in the 27th minute and that was enough to give the Welsh side three much-needed points.
Derby's Spanish midfielder Inigo Idiakez twice struck the bar but the home side created few chances in a disjointed and patchy performance.
Cardiff worked tirelessly and centre-backs Danny Gabbidon and James Collins won virtually everything in the air.
Derby were left to regret a bad miss by Morten Bisgaard before Thorne struck but there was little else in the way of clear chances for George Burley's team.
The manager has stated he is hoping to sign a foreign centre-half and Derby's pressing need to strengthen the defence was painfully illustrated in the first half.
The warning signs were clear when several poor clearances almost let Cardiff in but Burley must have been staggered at the goal his players presented to the visitors in the 27th minute.
After a long throw from Rhys Weston, Michael Johnson fell over and Tom Huddlestone missed his header to leave Thorne unmarked six yards out and he steered the ball over Lee Camp.
It was a cool finish but Derby should have been in front themselves had Bisgaard shown the same composure eight minutes earlier.
A sliced clearance from Weston fell to the Dane who was unmarked 15 yards out but he dragged a right-foot shot well wide.
Idiakez demonstrated his ability to strike a dead ball by sending a 30-yard free-kick against the crossbar and he also rattled Tony Warner's left-hand post.
The second half saw Derby huff and puff but despite another Idiakez free-kick which drifted just wide of Warner's right-hand post, Cardiff had few anxious moments.
Thorne should have scored a second when more poor defending allowed him time to turn but his shot was straight at Camp and there were also some half-chances for the visitors on the break.
Derby brought on Marco Reich and the German brought the first serious save out of Warner with a low 25-yard shot in the 74th minute but Cardiff held on with a degree of comfort.