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Derby manager Paul Jewell handed debuts to central defender James Tomkins and striker Luke Varney, but the visitors were soon up against it as the home side stormed into an early lead.
Robbie Blake's corner from the right-hand side found Steven Caldwell on the edge of the box and the Clarets skipper intelligently headed the ball to Kevin McDonald, who volleyed past Roy Carroll for his first goal since joining in the summer.
Burnley increased their lead on 15 minutes as Blake and Chris Eagles played a lovely one-two down the right-hand touchline before Eagles' cross to the near post was swept home by striker Martin Paterson, who was in the starting line-up for the first time in a month.
Varney had an opportunity to pull one back but fired wide from 15 yards.
The game was secured midway through the first half as Eagles teased Jordan Stewart yet again, before crossing low for Paterson to slide the ball past Carroll.
Derby's best hopes of salvaging something from the game lay with the elements as thick fog engulfed the ground, but it was the home side who continued to look the more threatening with McDonald sending Eagles clear to advance on Carroll, only to place his shot into the sidenetting.
Miles Addison was the only light to shine for the Rams with the midfield player going close on three occasions to scoring, the nearest of them being when he carefully place a shot beyond Jensen but was unlucky to see the ball strike a post.