Hazard put Chelsea ahead with a low shot before adding a superb second.
The 25-year-old forward now has seven goals this season – but Conte focused on his all-round contribution after a win that takes his side top.
“The most important thing I’m seeing with Eden is he’s fantastic with the ball and without the ball,” said Conte.
Hazard scored just four times in the league last season and cut an unhappy figure in what proved to be the final days of Jose Mourinho’s second spell as manager.
The Belgium international appears reborn under Conte and Saturday’s matchmarked the first time Hazard had scored two or more goals at Stamford Bridge in the league since February 2014.
“He played an impressive game. We all know he’s a talented player,” Conte said. “I see that he’s working a lot for the team and I think his team-mates are very happy for this.
“He’s a complete player, when he plays in this way – with the ball and without the ball.
“He must continue because he has great talent and he’s showing this in every game.”
Match Of The Day pundit Ian Wright said: “Eden Hazard was world class against Everton.
“I think Toffees boss Ronald Koeman picked the wrong day to pick three at the back.”
Conte’s side have been in searing form since switching to the Italian’s favoured 3-4-3 system, winning five games in a row, scoring 16 goals and conceding none.
“I’m pleased because when you win in this way it is fantastic,” he added. “All the players played in the right way with the ball and without the ball.
“We created many chances to score and it is also the fifth clean sheet in a row. That is fantastic because you look at the past and you can think that this is incredible to reach this result.
“It’s a pity that we have to stop now for the international break. I wanted to continue.”
‘Chelsea are title contenders’
Chelsea were disappointing last season, finishing 10th after winning the title in 2014-15 under Jose Mourinho.
However, Saturday’s win moved them to the top of the table, one point clear of Manchester City.
“It was one of the most dominant displays of football I have seen,” former Tottenham midfielder Jermaine Jenas said on Match of the Day.
“It is unbelievable how fast this Chelsea side has adapted to the way Conte wants them to play.
“The freedom they play with is scary so you can’t say they are not title contenders.”
Premier League Resuls: