KEVIN McDonald scored his first goal for Burnley before Martin Paterson's double established a comfortable lead at the break.
McDonald struck on six minutes from inside the D after he received Steven Caldwell's header when Derby failed to clear a corner.
Then Paterson stung County with two goals in seven minutes.
The Northern Ireland international picked up where he had left off following his brace at Barnsley on Monday night when his 10th goal of the season but the seal on a superb build-up down the right.
The leading scorer gave the Clarets a two-goal cushion midway through the first half with almost a carbon copy of his first, as he slid in to meet Chris Eagles' ball from the right and turn it past Roy Carroll.
Burnley's biggest battle in the second half is likely to be against the elements as the fog has descended quickly and thickly onto Turf Moor.
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