The Blues recovered from the shock of falling behind to Sol Bamba's early opener to maintain their 100% start to the new season.
Chelsea now sit joint top of the table with Jurgen Klopp's Liverpool who ran out 2-1 winners over Spurs at Wembley in today's early kick off.
But they had already shown a threat from set-pieces when Bamba headed just wide from a corner before taking the lead.
Neil Warnock's pre-match promise not to "shut-up shop" took shape when Bamba stunned an expectant Stamford Bridge crowd, prodding in defensive partner Sean Morrison's header. Pedro caused plenty of problems but was very wasteful with his shooting, whilst Giroud proved an excellent provider with two assists but failed to register a shot on target himself.
Chelsea's left flank was a constant threat as Hazard dovetailed with the rampaging Marcos Alonso from left-back.
Giroud was the only change to Chelsea's team from their 2-0 win over Bournemouth last time out, and the Frenchman more than justified his inclusion, winning each of his aerial duels against Cardiff's backline.
Those two may very well be remembered as Chelsea's two greatest ever players when Hazard is finished.
Kovacic was forced off in the second-half.
Chelsea rebuffed interest from Spanish giants Real Madrid and Barcelona for Hazard and Willian in the summer.
Hazard scored his third goal in the 80th minute via a penalty before Brazil worldwide Willian netted the fourth and last goal for the Blues to win the match 4-1.
His joyful penalty 10 minutes from time then furnished the 27-year-old master craftsman with the match ball, before Willian walloped home a fine fourth.