Spurs took control on 26 minutes as Serge Aurier teed up Son, whose goal made him only the second Spurs player to score in five consecutive home Premier League matches after Jermain Defoe in 2004.
Kane doubled the lead two minutes after the interval after wonderful approach play by Son.
The striker converted Eric Dier’s low cross on 59 minutes to surpass Teddy Sheringham to become Spurs’ leading PL scorer with 98 goals.
Christian Eriksen finished off a sweeping move on 81 minutes to round off a comfortable win.
Spurs move level on 44 points with fourth-placed Liverpool. Everton remain ninth.
Spurs: 21 Jan v Southampton (A)
Everton: 20 Jan v West Brom (H)