Chelsea manager, Maurizio Sarri had used Morata upfront during the opening four matches of the new season, but the 25-year-old only managed to find the net once, as his hard spell in England continues.
Despite Chelsea's fluency in attack, Sarri is aware the Stamford Bridge team must improve their defending.
It was significant that Olivier Giroud played a major part in two of Hazard's goals, as the big Frenchman justified Sarri's decision to start him ahead of Alvaro Morata.
The Chelsea forward has started the new Premier League season in stunning form, scoring five goals in five appearances.
"The manager just wants Chelsea to keep the ball, and then when we can find a solution we need to find good passes between the lines, like Jorginho, Kovacic and [Cesc] Fabregas can do", Hazard said after the Cardiff win.
"I do, I think he's fantastic". Hazard praised Giroud's ability to hold the ball and link play, saying: "He is a target man and maybe the best in the world". I felt that if Hazard was leaving Chelsea and soon, it would have been the summer just gone. I told him he can score 40 goals.
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The former Lille star won the PFA player of the year award in 2015 after Hazard fired Chelsea FC to the Premier League title.
"Sarri has raised his concerns around our defending and at times you can see why!"
"I'm talking over a four or five-year period if I think 'who's the man?' - [and] I think he's fantastic. But I also think he can still improve more". For their characteristics, they are different.
Hazard is the early pace-setter in the race for the Golden Boot, with one more goal than both Liverpool's Sadio Mane and Fulham's Aleksandar Mitrovic.
Is Hazard really the best in Europe or even the best European?
"Certainly, after this World Cup, I can decide if I want to stay or go, but Chelsea will have the final decision".
"Playing the top six is always hard, but we're enjoying it - that's why we're here and we're going to try to do our best against any team".