Hazard and company made it six points from a possible six in the English top-flight this weekend after battling to earn a late 2-1 away win against Watford.
Diego Costa was once again the hero, netting the winner after close-season signing Michy Batshuayi levelled things up. Earlier, Etienne Capoue scored his second of the campaign in superb fashion to put the hosts ahead at Vicarage Road.
Hazard insists that the results are no fluke and that Chelsea have been deserving winners in their opening competitive fixtures, attributing their success to how the players have been applying themselves under former Italy boss Conte.
"The attitude is fantastic, even in training everyone wants to win games," Hazard told Chelsea's official website.
"That is why now we are winning, it's always difficult to come back when they score but we did great.
"We played a good second half and we scored two great goals - at the end I think we deserved to win.
"It's just the start of the season but if we want to stay at the top we have to win. Both Manchester teams won, so we had to win and we did."
New arrival N'Golo Kante also believes this attitude and Conte are key to Chelsea's current form.
"We know the coach has his idea of football and he tries to teach it to us," Kante told Chelsea's offical website.
"We try to win all the games like he wants, he's a good manager, he believes in his team and we try to give everything for him.
"It is early, we have a good team, but of course we want to be the champions."