Jacob Butterfield scored both goals in the first half with two quality finishes as the visitors made the most of the space afforded to them by the home side.
Butterfield hit two cultured left-foot shots as Derby made the Tigers look second best and took over first place in the table from their hosts.
Hull’s best efforts came from Shaun Maloney and Abel Hernandez but they failed to pose the same threat as the visitors and as a result lost at home for the first time in all competitions this season.
Where Hull had made fellow top-six sides Birmingham and Middlesbrough look second best in front of their own fans, this time it was the Tigers’ turn to be dominated.
Derby were the better side and it would not have been an injustice if their winning margin had been greater.
Clement said: “I’m really pleased. I thought it was a really terrific effort.
“We’ve come to a place with the best defence in the league and scored two goals.
“Maybe not our best (performance) in terms of possession football, chances created, but in terms of a professional performance against a good side.
“One of the big messages was play with confidence, we’re not coming here to sit on the edge of our box and soak up pressure.
“In terms of our own confidence and the way we’re moving it’s very positive.”
Clement praised Butterfield, who took both goals with composure.
“We knew that (Butterfield could score) before he came here,” he said. “That’s one of the reasons we brought him here.
“He has taken time to settle based on the way we are asking him to play. That’s part of the reason we’re seeing the best of him now.”
Hull manager Steve Bruce saw his side lose their unbeaten home record in all competitions this season and admitted he had got his changes wrong after losing defenders Michael Dawson and Andy Robertson to suspension.
“The way we were in the first 20-25 minutes in difficult conditions, we made far too many mistakes,” admitted Bruce.
“I have to question myself the way I set us up. In hindsight I think I would have done something different. I think I’ve taken us out of our comfort zone. We were nowhere near the level which is required.
“The decision I had was (Moses) Odubajo has played at left-back before. I was trying to fit (Mo) Diame in and Maloney in and (ended up) taking away the threat on the right hand side of Odubajo and (Ahmed) Elmohamady.
“It’s a reminder of how difficult it is. Derby are easily the best team we’ve seen here. They’ve beaten us comfortably.”