The visitors dominated the first half but could not find a way past goalkeeper Kepa Arrizabalaga. City were made to pay just before half-time when Kante opened the scoring.
Eden Hazard managed to find the Frenchman in the penalty area, and he smashed the ball into the top corner to give the Blues the lead at the break.
Manchester City struggled to create chances in the second half, and Chelsea made the game safe with 12 minutes of normal time remaining.
Hazard swung in a corner from the left for Luiz to head home and secure all three points for Maurizio Sarri's men.
Hazard Goes Missing in Big Game Again
Chelsea manager Maurizio Sarri risked alienating Hazard by playing him as a false nine against Manchester City.
The Belgian spoke last season about his frustration at playing the role after his team's 1-0 defeat to City at the Etihad Stadium, per Telegraph Sport.
Once again he found it tough going against the Sky Blues; he rarely saw the ball and was frequently left isolated in attack.
Simon Johnson at the Evening Standard noted how Chelsea struggled to find their talisman:
Yet he still managed to end the game with two assists. He found Kante for the opening goal, although there was some suspicion over whether his pass was intended for the midfielder:
His corner also set up Luiz for Chelsea's second, which secured the win. However, EiF Soccer highlighted how little he was involved in the game:
Goal's Nizaar Kinsella offered his view of Hazard's performance:
The victory will vindicate Sarri's team selection for this game. However, Hazard does not seem to enjoy being played as a false nine, and it is not a position which gets the best out of the Belgian.
Man City Still Title Favourites Despite Loss
Manchester City suffered their first Premier League defeat of the season on Saturday and have been knocked off the top of the table by Liverpool.
Guardiola's side now lie second and trail the Reds by a single point after 16 games. However, despite the defeat to Chelsea, they should still be considered title favourites.
The visitors were missing some key players for their trip to west London. Top scorer Sergio Aguero was left out because of injury, while key midfielder Kevin De Bruyne is still sidelined.
Yet City were still the better team in the first half and can consider themselves unfortunate to have gone in at half-time behind.
Miguel Delaney at The Independent said they might have become complacent:
Manchester City's lack of a response in the second half will concern Guardiola, as will their inability to win matches after going behind away from home:
However, the champions still have the best squad in the top flight, and they are a class above both Chelsea and Liverpool, according to ESPN FC's Liam Twomey:
The defeat may ultimately serve Guardiola's team well. It shows they cannot afford to be complacent and still have areas to improve if they are to retain their title.
Kante Shows He Can Play More Attacking Role
Sarri's use of Kante has prompted much discussion this season, with the Frenchman moved from his usual holding role following the summer arrival of Jorginho.
Kante is widely regarded as one of the best in the business in his position, but he's been asked to play a more attacking role by Sarri this season and there have been question marks over his suitability.
However, the 27-year-old proved he has what it takes to play the position against Manchester City. He was in the right place to power home the opening goal with an exquisite finish.
Vaishali Bhardwaj at the Evening Standard offered her view on his goal:
Squawka Football highlighted his improved attacking contribution this term:
The goal seemed to fill the World Cup winner with confidence, as he put in a much improved display in the second half.
His break forward and pass to Willian saw the hosts have a chance to double their lead, but the Brazilian's shot was saved by goalkeeper Ederson.
It was a timely performance from Kante, which should remove some of the doubts over his position in Sarri's system.
Manchester City's next fixture is against Hoffenheim in the UEFA Champions League on Wednesday. Chelsea play away at Hungarian champions Vidi in the Europa League on Thursday.