Lee Morris gave the Derby fans a long-awaited home win to celebrate, with a well-taken first-half goal as Burnley ended the match with ten men.
The sending off of Arthur Gnohere in stoppage time looked harsh and the Lancashire club will ask referee Uriah Rennie to watch a video of the incident.
An Ian Taylor penalty at the very end of the match finally finished off Burnley, but it might have been different but for a brilliant save from Lee Grant in the 16th minute.
David May's glancing header from Robbie Blake's free-kick was heading for the bottom corner, until Lee Grant plunged to his left to push the ball to safety.
It was an outstanding reflex save from the England Under-21 keeper and four minutes later his team were in front.
The excellent Taylor threaded the ball through Burnley's square back line and Morris timed his run perfectly to go clear before placing his shot over Brian Jensen from ten yards.
Glen Little was a major influence in the second half and Blake constantly threatened, but Burnley could not find a finish.
Little put Richard Chaplow in on the Derby left two minutes after the break, but Lee Grant made another good save, this time diving to his right, and there were more chances for the visitors.
An excellent cross from Little was heading for Ian Moore until Chaplow took it away from the striker and Michael Johnson made an excellent saving tackle to block Graham Branch.
Moore headed over when Little again delivered a good cross from the right, and the striker fired wide when the ball broke to him just inside the Derby box in the 79th minute.
But, Derby hung on and in stoppage time, Burnley were incensed when Gnohere was shown a straight red card when he tussled with Danny Dichio.
Rennie decided Dichio would have been clear but the decision was a harsh one, and Burnley were arguing again minutes later when Morris went flying and the referee pointed to the spot.
Taylor calmly stepped forward to rifle the ball inside Jensen's right hand post and there was barely enough time to kick-off before Derby's fans could at last hail a victory at Pride Park.