The striker looked rich in confidence after his drought-breaking goal for France last weekend as a pair of delicate touches late in the first half sliced open a Cardiff defence that until then appeared in good order.
Moments later Willian produced his own moment of magic with a wonderful curling effort from 20 yards that bent into the top corner.
Hazard scored twice in a devastating seven-minute spell before the break to turn the game on its head, both goals courtesy of superb link-up play from Giroud, who was making his first start of the season at the expense of Alvaro Morata.
Chelsea, who lead Jurgen Klopp's side in the table on goal difference, make the short trip to West Ham a week on Sunday in their next league game.
Chelsea manager Maurizio Sarri has spoken about the possibility of one the Blues legends returning to the club.
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Sarri spent the September worldwide break in England, dividing his time between walking his dog Ciro around the large garden of his new house a short drive from Chelsea's training ground in Surrey - "Similar to my name", he joked - and studying video of his team's upcoming opponents.
As a team, though, the Blues were not at their fluid best despite matching their best-ever start to a Premier League season with a fifth win from five. "But spend less energy far from the goal and play in the last 25 metres".
Willian put the icing on the cake for Chelsea towards the end of the 90 minutes with a sumptuous strike that the Neil Etheridge could do nothing about.
"The next logical step was to continue with Chelsea". Cardiff simply had no answers once the Belgian artisan hit his creative best.
Having got in front, Chelsea took their foot off the gas at the start of the second-half and could have been made to pay when Ralls and Bobby Reid shot just wide from the edge of the area.