The Belgium international completed his hat trick 10 minutes from time and Willian added gloss to the scoreline in the 83rd minute.
Chelsea boss Maurizio Sarri praised Hazard for a man-of-the-match performance.
"I thought that Hazard was one of the best players in Europe," said the 59-year-old Italian. "But now I change my mind because maybe he is the best."
The romp past Cardiff mainitaned Chelsea’s 100 per cent start to the season and propelled them to top spot on goal difference. Liverpool have also won their opening five games.
The latest victory was a 2-1 win at Tottenham thanks to goals from Georginio Wijnaldum and Roberto Firmino.
Liverpool have never won their first five games in the Premier League era. Despite the sequence, Liverpool boss Jurgen Klopp said he wanted to calm talk of a title winning surge.
"Nobody will play the perfect season,” he said. “It's still early. We have won all five games and improved. I like that development. Now we have to prove that and do it again and again."
Champions Manchester City moved up to third following a 3-0 breeze past Fulham.
Pep Guardiola started Leroy Sane for the first time this campaign and last season's Premier League young player of the year repaid the Spaniard’s faith by slotting in the first goal after two minutes.
David Silva added the second mid way through the first half and Raheem Sterling made it 3-0 just after half-time.
"In the period he didn't play, we never doubted Leroy's quality," said Guardiola. "He is 22 and this little bit of up and down can sometimes happen at this age. But I'm delighted with his performance, a big compliment to him."
Watford dropped to fourth after suffering their first defeat of the season. Manchester United beat them 2-1.