A fifth victory from five matches this season took Chelsea top of the Premier League table.
A flawless start through five games is not unheard of in the Premier League as Chelsea themselves have done it four times, though both of Liverpool's previous five-for-five came in the old First Division.
Hazard completed his hat-trick from the penalty spot before Willian's stunning strike completed the rout seven minutes from time.
Azpilicueta has captained Chelsea so far this season, but that may not be an indication that he's Sarri's number one choice.
"The next logical step was to continue with Chelsea". I am very open with him because he is the history of the club. Giroud laid on the assists for the first two of his teammate's three goals on the day.
But Sarri, whose Chelsea side have defied expectations and could be a surprise challenger for the title come May, believes it's still only City and Liverpool who will be fighting for the top prize.
The Bluebirds' defence and midfield were outstanding, with the one blotch on an impressive performance being Sol Bamba's mistimed lunge on Willian. Cardiff went into the global break with a 3-2 loss to Arsenal, a game that earned the Gunners their second win of the season.
The headlines won't tell the whole full story tomorrow, with a scoreline that flattered the hosts, but it was a tough lesson to learn for the Premier League newcomers.
On paper, this game looks like a straightforward win for Chelsea. The midfield as a whole provided a good screen for the defence and did well to actually produce some good attacking positions.
Sarri has been impressed with the Brazilian defender, as he said: "David has a big future here - he will be very useful for us".
Chelsea are favourites to maintain their flawless start to the league season at Stamford Bridge against Neil Warnock's men, who are winless in their opening four games.