The England captain slotted home the opening goal against the Premier League champions to move past Jimmy Greaves, who scored 266 goals for Spurs between 1961 and 1970.
The 29-year-old is now also just the third player to net 200 Premier League goals, after Alan Shearer (260) and Wayne Rooney (208).
Kane is also level with Wayne Rooney as England's joint record goalscorer after bagging his 53rd international goal in the World Cup quarter-final defeat against France in December.
However, despite his heroics for club and country, Kane is yet to win a major trophy in his career.
Greaves, who died aged 81 in 2021, is regarded as one of the most natural goal scorers in football history.
A member of England's 1966 World Cup-winning squad, who netted 44 times for his country, Greaves is the highest scorer in English top-flight history with 357 goals.