First half goals from Danny Ings and Sam Vokes put the visitors in the box seat and after Tom Heaton saved a Johnny Russell penalty, former Derby defender Jason Shackell clinched the points with a 73rd minute penalty.
Burnley had not lost to Derby since January 2007, a run which included three wins at Pride Park, and they came close to scoring in the ninth minute when Michael Duff headed a free kick narrowly wide.
But they scored five minutes later when Keith Treacy hooked the ball forward and Ings muscled his way past Jake Buxton to steer a low shot across former Burnley 'keeper Lee Grant from 10 yards.
Derby were struggling to find any fluency as Burnley closed them down at every opportunity and the visitors extended their lead in the 32nd minute with a goal that left Nigel Clough holding his head in anguish.
A long ball to the back post from Kieran Trippier was headed across his own area by Derby right back Kieron Freeman and although Will Hughes tried to clear, Vokes bundled the ball in from six yards.
Derby had a chance to get back in the game three minutes before half-time when Chris Martin and Will Hughes rode tackles to force the ball through to Johnny Russell but he shot wide from eight yards.
Freeman was replaced by on-loan Spurs defender Adam Smith for the second half and Derby had another chance to score in the 52nd minute when Trippier's attempt to head the ball let Russell in on the left but he shot into the side netting from a tight angle.
Derby were getting more possession and in the 63rd minute, they had a great chance to reduce the arrears when Shackell was ruled to have tripped Martin and referee Andrew Madley awarded a penalty.
Shackell looked to have got the ball and Burnley boss Sean Dyche reacted furiously on the touchline but Tom Heaton made a superb instinctive save by throwing up his left hand to block Russell's spot kick.
Voges was inches away from a third minutes later when he headed a free kick just past Grant's right hand post with the goalkeeper stranded and Grant kept the home side in it with a point blank save from Vokes in the 72nd minute.
But Derby's relief was short-lived because from the resulting corner, the ball reached Shackell at the back post and he smashed a volley from 10 yards inside the left-hand upright.
Ings thought he had scored a fourth five minutes later when Junior Stanislas played him in but he had strayed marginally offside although it was one of the few mistakes Burnley made on a highly satisfactory afternoon for Dyche's men.