First half goals from Craig Bryson and Jamie Ward put Derby in control and a Richard Keogh header just before the hour finished off Huddersfield who had skipper Peter Clarke taken to hospital for a precautionary scan after he suffered concussion.
Huddersfield caretaker boss Mark Lillis had no complaints about the defeat to one of his former clubs.
“Derby played very well and all credit to Nigel (Clough), he’s doing well and they looked like a top six team,” he said.
“It’s been a tough week for us and we caught them on a good day and they deserved the win. But there’s no lack of application or commitment on the pitch and I am proud of the players.”