Danny Ings and Sam Vokes got the opening goals that put Burnley on course for a fourth consecutive victory at Pride Park, stretching their unbeaten run against Derby to nine games.
Former Derby defender Jason Shackell smashed in a third in the 73rd minute although the home side could have got back in it when Johnny Russell had a 63rd-minute penalty saved by Tom Heaton.
Dyche said: "It was a very good performance.The link all managers are looking for is when the physicality meets tactical organisation meets with individual and team quality and I thought we found that for a lot of the game.
"Danny (Ings) is really alive at the moment and he's enjoying it. We spoke a lot to him last year and during the summer about what we think he can achieve and he's taken a lot on board.
"I must say that he's getting the plaudits and rightly so but I will put Sam Vokes into the mix, I thought today he was absolutely tremendous and for the last 25 minutes was unplayable. He's developing well and I think he's enjoying his football."
But Dyche was astonished by referee Andrew Madley's decision to award the penalty for Shackell's challenge on Chris Martin.
"In two weeks I've seen two of the most incredible moments in my time in the game and I don't know what the words are," he said.
"I think it's only fair to mention it because we all come in and talk about decisions that affect a game when we've lost so even though we've won I must mention it because it's not fair to only pick on these things when you lose.
"That could have affected the outcome more because of the feel of the stadium because if they score it's a lifeline and the players are suddenly lifted. I must say it was a fantastic tackle and a brilliant save."
Derby manager Nigel Clough admitted: "I'm very disappointed with the defending in the first half. We have been good going forward and good defensively but today we were poor in both areas.
"When you're 1-0 down after 14 minutes at home you are up against it and then you give a second one away.
"It was down to individual errors and we brought Kieron (Freeman) off at half-time, we thought both goals came from his area and he should have done better, but it's about the team and we never seemed to get going.
"You have to give Burnley credit and it was never going to be comfortable but if you give goals away you don't give yourself a chance. In the second half I thought for 25 minutes we were very good and had chances to get back in the game, the penalty being the most obvious one but we didn't quite manage it.
"I didn't think it was a penalty but we miss penalties at crucial times in games."
Clough revealed he is looking to the loan market after midfielder Jeff Hendrick was ruled out for 12 weeks with a foot injury.
"He's chipped a bone at the top of his foot and will have a small procedure on Monday morning and will be in a boot for six weeks and start his rehab after that," he said.
"We missed him today, we missed his driving runs and his impetus but we will have get used to it for 12 weeks."