Sarri joins elite club after Hazard hat trick for Chelsea
Sol Bamba shocked Chelsea with Cardiff's first away goal of the season, but Hazard's treble and a late goal by Willian saw Maurizio Sarri became the fourth manager to win his first five Premier League games. He joined an elite club of Carlo Ancelotti (Chelsea), Pep Guardiola (Manchester City) and Craig Shakespeare (Leicester).
Chelsea kept pace with Liverpool at the top of the table.
Former Napoli manager Sarri's fine start to life in England looked to be under threat when Cardiff took the lead after 16 minutes at Stamford Bridge. Bamba latched onto a flick-on from fellow defender Sean Morrison.
Hazard, who has scored or assisted in each of Chelsea's four games this season, took over the game shortly before halftime.
The Belgium captain received the ball just outside the Cardiff box in the 37th and surged past a defender before driving a powerful finish across goal to equalize.
Chelsea rarely relinquished control from that moment on, but it wasn't until substitute Willian won a penalty in the 80th that the Blues put the game beyond doubt.
Hazard sent Cardiff goalkeeper Neil Etheridge, who had already saved two penalties this season, the wrong way to complete the second Premier League hat trick of his Chelsea career.
Willian then added a goal of his own three minutes later, curling the ball into the top corner from the edge of the box.
Cardiff has two points from five games.