But a brace from Hazard before half-time put Chelsea ahead at Stamford Bridge going into the break.
Hazard has now scored five goals in five league matches this season, while also providing two assists, and he became only the fourth player to score more than one hat-trick for Chelsea in the Premier League, alongside Didier Drogba, Frank Lampard and Jimmy Floyd Hasselbaink.
He has carried on his spectacular form of the previous campaign as he has already netted 4 goals in 5 league games so far this season.
World Cup-winning striker Giroud laid on two goals for Hazard as the Belgium playmaker bagged a hat-trick in the Blues' 4-1 rout of Cardiff at Stamford Bridge on Saturday.
Asked if Hazard can win the Golden Boot, Sarri replied: "I think so". "So I think it's normal that in this period we have some defensive problems".
Hazard 'maybe' the best in Europe, says Chelsea boss Sarri
He was unlucky not to be named player of the World Cup. "I think we are very risky going forward, but not so solid defensively". Asked which teams are in title contention, Sarri said: "At the moment I can answer City or Liverpool, at the moment.
"Maybe because he switched off a little under José Mourinho he is not viewed as highly as he should be, but Chelsea fans should know that they are watching not only one of the best players in Europe at the moment, but the best they have had". We have spoken and I told him he can score 40 goals. He has to improve something, but he can do it.
"We saw a year ago Salah fight for it and they play more or less the same position, as a winger coming inside the pitch", Alonso said. That has led Chelsea manager Maurizio Sarri to claim the Belgian is the best player in Europe.
He's having a wonderful 2018 in general, captaining Belgium to the World Cup semis, and now helping Chelsea achieve a ideal start to Sarri's debut season!
"After 20 minutes the score was 1-0 for Cardiff, but we just kept playing our football and then, when we have the chance, we need to score, and that's what we did".
One complaint of the Belgian, who grew up idolising Zinedine Zidane, has always been that he never manages to score enough goals given his level of influence and talent.