Following a tight affair in the first half, Chelsea boss Thomas Tuchel brought on Kante after the break.
The visitors scored three goals to seal the victory.
Chelsea continued their unbeaten start to the Premier League campaign and go level on points with Liverpool.
Spurs have now lost back-to-back league games after winning their first three under new manager Nuno Espirito Santo.
Another superb team performance, but who gets your #TOTCHE Man of the Match vote today? 💪
— Chelsea FC (@ChelseaFC) September 19, 2021
The London derby was also the world’s first net-zero carbon football match at an elite level.
The project aimed to educate fans on the role of sport in addressing climate change.
while supporters at the stadium were encouraged to choose plant-based food options and recycle.
Before kickoff, both sets of players and supporters gave an emotional minute’s applause in memory of former Spurs and Chelsea striker Jimmy Greaves, who died on Sunday at age 81.
Spurs enjoyed the better of the first half with few clear-cut chances
Spurs came closest to scoring after 33 minutes when Son was denied from close range by Chelsea goalkeeper Kepa Arrizabalaga.
Kante replaced Mason Mount after the break which saw Chelsea dominate.
Chelsea took the lead after 49 minutes when Silva headed in from Marcus Alonso’s corner.
Three minutes later, Alonso almost doubled Chelsea’s lead but his strike was brilliantly clear off the line by Eric Dier.
Just before the hour mark, Dier was left in an unfortunate position when Kante’s shot deflected off him into the bottom corner.
Silva almost grabbed a second from another corner after 76 minutes but Hugo Lloris parried his header wide.
Rudiger made it 3-0 in stoppage time with a well-taken finish from Timo Werner’s low cross.