CHARLIE Austin scored his 23rd goal of the season to give the Clarets a half-time lead.
The striker's 39th minute deflected effort made him the first Burnley player since Andy Payton in the 1999/2000 season to reach 20 league goals – in only the 23rd Championship game.
Martin Paterson might have put Sean Dyche's men in front in the fourth minute after being released by an excellent Danny Ings ball, but Adam Legzdins saved with his legs.
The Clarets probed and gave Derby plenty of defending to do in the early stages, but the visitors recovered to create a handful of half chances.
But Burnley came back into it after a lull, with Austin causing problems.
First the top scorer had a header deflected over from Trippier's cross, but the two combined again a minute later.
Austin didn't make a great connection but Legzdins was beaten by a wicked deflection.