Matej Vydra broke the deadlock for the Rams in the 15th minute with a free kick from the edge of the area, but the visitors had the chance to equalise when they were awarded a penalty for a foul on Ola Aina moments later.
Sebastian Larsson put his effort well over the crossbar, and things quickly went from bad to worse for Hull as Vydra fired into the bottom corner on 33 minutes to double his and Derby's tally for the evening.
The hosts made it 3-0 in the 38th minute when Curtis Davies rose highest in the box to head home a corner, and it was four right on the stroke of half time as Bradley Johnson guided in another corner at the far post.
Johnson rounded off the scoring just before the hour mark following good work by Andreas Weimann, the former Aston Villa man providing a cross from out wide for the striker to smash home for his second of the night.
The result sees Derby climb up to fourth place in the Championship, while Hull drop down to 10th. body check tags ::