Kane struck in the 15th minute to give his side the lead and his feat was warmly celebrated by the Spurs fans in the stadium.
England captain Kane had matched the tally of the late Jimmy Greaves when he scored the winner at Fulham last month.
Greaves's record had stood since 1970.
Kane's 267 goals have come in 416 appearances for the club in all competitions while Greaves played 379 games.
The goal was also his 200th in the Premier League.