The Belgian scored twice in the first half to cancel out Sol Bamba's surprise opener for the Bluebirds, who were unable to push on from their bright start.
A third Hazard goal followed from the penalty spot 10 minutes from time, before Willian came off the bench to round off the scoring in style.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Kepa; Azpilicueta, Rudiger, Luiz, Alonso; Jorginho, Kante, Kovacic; Pedro, Giroud, Hazard
SUBS: Caballero, Zappacosta, Christensen, Drinkwater, Barkley, Willian, Morata
STARTING XI: Etheridge; Manga, Bamba, Morrison, Bennett; Camarasa, Ralls, Arter, Hoilett; Ward, Reid
SUBS: Murphy, Peltier, Richards, Cunningham, Paterson, Zohore, Madine
Maurizio Sarri: "My feeling is that we are not a very solid team in the defensive phase. We can improve and that's what I feel in training. The title challengers? At the moment I can answer Manchester City or Liverpool. We need another step I think to be at the same level. I think so, but I hope not. It's very difficult. The gap last season was 30 points so I think to go above 30 points in one season is very, very difficult. I think we must improve."
Neil Warnock: "The top sides always have a lot of possession so we're going to be under the cosh for a long time, but we've got to find a remedy. We've earned the right to play against teams like Chelsea. It'll be interesting to see how we cope at a packed Stamford Bridge. It's one where we've got to get the best out of what we've got. I don't want to go there and not have a shot on target, but we've got to have players at their best abilities to give them a game."
CHELSEA SUBS: Caballero, Zappacosta, Christensen, Drinkwater, Barkley, Willian, Morata
CARDIFF CITY SUBS: Murphy, Peltier, Richards, Cunningham, Paterson, Zohore, Madine