Bournemouth held firm for much of the match but substitute Pedro proved the difference in the 72nd minute by making it 1-0 at Stamford Bridge, with Hazard then adding a second after a one-two with Marcos Alonso.
Chelsea's perfect start has surprised many, including manager Maurizio Sarri, who thought it might take up to three months to implement his new footballing philosophy at the club. Sarri has stopped short in calling his side title contenders but Hazard was less shy as the Belgium ace heads into the international break.
"Of course, in the end we want to compete for the first three places," Hazard told reporters at Stamford Bridge. "We want to be champions at the end although we know it will be hard because Manchester City, Liverpool and Tottenham are very strong. So we will see at the end, but we want to be at the top."
"We can improve [on the Bournemouth game], of course. Today we didn’t concede a goal - that’s a good point. We scored two, maybe we should have scored more - like always. I think we can move the ball quicker - in the first we were a bit slower. We can improve. We have the confidence.
"We have the international break now. We can rest a bit some players. We have a lot of hard games when we get back."
Hazard has two goals and two assists in his first four games under Sarri, which is made even more impressive by the fact that he only started in two of them due to a late return from this summer's World Cup in Russia.
There is a new found positivity at Chelsea, as Sarri relaxes some of the rules and eases the tension in the dressing room that was present in the final year of Antonio Conte's reign at the club.
The change of boss seems to be helping several players bounce back from last season, where Chelsea finished fifth in the Premier League. Hazard is enjoying the new style of football and thinks that keeping possession is the major shift from an attacking point of view.
"I think the big change is that we try to keep the ball more often," he continued. "So that’s why we have more of the ball, we create more chances, we are scoring goals. But it’s only four games now with the new manager - so we will see at the end of the season.
"It is so simple we just need to play quicker, to move forward quicker - the manager doesn’t like us to just keep the ball at the back. He wants the ball to keep moving forward, so we are trying to do this in training, so we can do it when we have a game."
The change, according to Hazard, may be why Chelsea has seen success scoring late this season.
He added: "I think this is the Premier League where every game is hard, we just need to not go forward too quickly. You just need to keep the ball, like I said before, we like to keep the ball now and then near the end of the game, maybe the opponent is tired.
"Maybe that’s why we are scoring late in the games. We did it at Newcastle, Bournemouth, Arsenal, so, yeah, we just need to be patient. When we have the ball we create chances and then at the end, if we need to score a goal, we have to score.
"When you play for Chelsea, at the end of the game the most important thing is to win the game. We are just focused on that. We want to play a good game, keep the ball all the time, press high - because the manager also wants us to press high when we lose the ball.
"We just want to win games."