Gary Hooper struck twice in the first half and Kieran Lee added a third late on to lift the home crowd following back-to-back defeats at the hands of Sheffield United and Birmingham.
The opening goal came in the 25th minute when Ross Wallace’s free-kick was headed down by Tom Lees and Hooper provided the finishing touch from close range.
Lee was unfortunate to have an effort ruled out with television replays showing that he should not have been given offside.
It was 2-0 when Liam Palmer delivered a deep cross which was headed back across the face of goal by Steven Fletcher and Hooper nodded in off the inside of a post.
Lee completed the scoring eight minutes from time with a fine shot from 20 yards after receiving Eunan O’Kane’s attempted clearance.
Carvalhal said: “I think it was a very good game, which was a good promotion for the Championship.
“The quality is exactly what we expect. The performance was a good level against a strong side who have done very well so far. What made a big difference in this game is that we scored first. After that, we managed the game very well.
“When you have one goal in the Championship, you have a big advantage. It makes a massive difference in derby matches when emotions are high.
“Gary Hooper did very well and all of the team performed very well. Gary did fantastic teamwork as well as score goals.
“I am very resilient and I don’t give up easily. I am here to fight for Sheffield Wednesday and after suffering two defeats, I don’t go around thinking we can’t achieve promotion.”
Leeds head coach Thomas Christiansen admits his side need to improve defensively after conceding three goals for the second consecutive game.
He said: “In the first 20 to 25 minutes, we did quite well and had opportunities, but we conceded two goals too easily.
“In the first half, they had two opportunities and scored. We were too soft in both areas so we have to improve a lot in that sense.
“We gave too much space. We were defending back instead of defending up, which makes you lose the second balls
“We spoke about (Barry) Bannan as being a key player we had to stop, but we were not able to do that.
“We have played against good teams and won. When you are competing in a league like this, you have to be ready to compete 100 per cent.
“We are not strong enough and we are not competing as we should, especially in these situations.
“I will analyse the situation and look forward before for our next game against Reading.”