The Belgium international scored twice to help the Premier League champions come from a goal down to beat Rafael Benitez's side at Stamford Bridge and move level on points with second-place Manchester United ahead of their clash with Arsenal.
Hazard now has four goals in as many league games and Conte believes he is relishing his free role behind striker Alvaro Morata.
"I think he played a really good game," Conte said. "I think he enjoyed a lot playing this type of football. He is an important player as we can change our system. He can play as a second striker, he can play as number 10.
"Eden and Alvaro showed a great link and I saw a lot of good combination play. I am happy."
Hazard cancelled out Dwight Gayle's opener and capped the victory with a 'Panenka' penalty in the second half after Morata's header had made it 2-1.
Conte has no problem with the manner in which Hazard took the spot-kick but he warned him to be careful of goalkeepers wising up to his ideas.
"The most important thing for me is score the penalty and then you can decide what you want and how you want to kick," he said.
"Next time, he must have great attention, as the goalkeeper studies the players who take the penalty. I repeat, for me the most important thing is to score. It happened."
"There are two teams to qualify for the next round," he said. "England and Belgium are favourites to do this in the World Cup. It will be special to see this game, England against Belgium; if I have the possibility, I would like to watch this game.
"Gary [Cahill] knows very well Hazard's skill; for this reason, he must pay great attention."
Chelsea's win moved them back to within eight points of leaders Manchester City, who face West Ham on Sunday, but Conte admits Pep Guardiola's side will be difficult to catch unless their form falters.
"You know very well, in this league, there is a team doing extraordinary things and that is Manchester City," Conte said.
"At the same time, it is important to look at ourselves and go step by step and go game by game."