Willian scored the fourth and final goal, with Sol Bamba actually giving the newly-promoted visitors the lead in the first-half.
The Blues have started the season well, winning all four of their games to date.
Chelsea's Eden Hazard scores his side's first goal during their English Premier League soccer match between Chelsea and Cardiff City at Stamford Bridge stadium in London Saturday, Sept. 15, 2018. I think so. When he gets the ball, he can hold it and we can go with him.
Eden Hazard is now the top goal scorer in the Premier League.
Watford had also taken 12 points out of 12, but Javi Gracia's Hornets lost for the first time this term by going down 2-1 at home to Manchester United.
"We need to improve, and we can improve".
Spurs paid a heavy price for the absence of captain Hugo Lloris through injury as stand-in goalkeeper Michel Vorm flapped at a corner six minutes before the break and Georginio Wijnaldum looped a header over the line before Vorm could scramble clear.
Arter was a little quick to the ground though, leaving his covering players exposed and producing some needless fouls.
On paper, this game looks like a straightforward win for Chelsea. However, they shouldn't underestimate Cardiff.
However, for two teams to manage it is unheard of - this is first season in Premier League history where a pair of clubs managed flawless starts through five games.
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. Pedro's cross found Olivier Giroud, who laid the ball off for Hazard, allowing him to unleash a strike which deflected in off Bamba.