Tottenham came close to going 1-0 up against Chelsea, only to find themselves trailing soon after.
His early header from an Aaron Lennon cross beat goalkeeper Thibaut Courtois, only to be denied by the bar.
It could prove a decisive miss, with the game turning soon after.
Goals from Eden Hazard and Didier Drogba put Chelsea 2-0 up after 22 minutes, leaving Spurs with an uphill task.
Kane is leading the line on his own with striker Roberto Soldado surprisingly left out after breaking his goal drought at the weekend.
The last time Spurs won at Stamford Bridge was back in 1990, with Kane not even born at the time.
Tottenham lost 4-0 during their last visit to the ground, and the early scoreline does not bode well for their chances of a similar embarrassment. They have however come from behind to win in their last two league games, against Hull and Everton.