Then, after Reece James put Chelsea back in front in the 77th, Tuchel set off on a sprint past Conte and down the touchline, clenching his fist in pure delight.
Kane's goal came in the sixth of seven added-on minutes, the striker glancing in a header that took a touch off the thigh of James before going into the net.
Kalidou Koulibaly had put Chelsea ahead in the 19th minute by meeting a deep corner from Marc Cucurella with a stunning volley that flew high into the net for his first goal since joining in the offseason from Napoli.
Tottenham, which only came to life after the introduction of Richarlison, ended a run of five straight losses to Chelsea in all competitions but remained stuck on just one victory at Stamford Bridge since the Premier League started in 1992.
Both teams have four points from two games.