Kane, the Premier League's top scorer with 18 goals and December's player of the month, recently suggested that Spurs have to start winning trophies if they want to retain his services amid reported interest by Real Madrid.
I've seen a lot of fantastic Son performances since the South Korean joined Spurs in 2015, few of which better than his near ideal display this evening.
Everton manager Sam Allardyce brought on former Spurs winger Aaron Lennon, who was given a superb reception by the home fans, but the pattern of the game remained the same as Spurs threatened again and Son hit the post.
Son Heung-min scored the opener in the first half before Kane's brace.
Wayne Rooney then dragged an effort wide at the other end and looked to have given Everton the lead in the 22nd minute as he turned Tosun's flick-on beyond Hugo Lloris from point-blank range, only to be correctly denied by the offside flag.
The goal against Everton also made Son only the second player to score in five consecutive home Premier League matches for the Spurs after Jermain Defoe in 2004.
"I'm so happy because it's three points that give us the belief and the confidence and of course the position in the table that is so close to Chelsea, Liverpool and Manchester United and the possibility to fight for a place in the top four". I hadn't seen it since I got here. Then, when the second goal goes in and it's probably offside, that doesn't allow us to throw the towel in for me and not do the right things.
Just 29.6% of Everton's Premier League points this season have come away from home (8/27), the lowest ratio in the division.
"Maybe I have to take the responsibility for playing too many attack-minded players".
"It was a shock second-half performance".
- This was Tottenham's biggest margin of victory in a game against Everton since a 10-4 win in October 1958.
He continually powered towards goal whenever he had possession, linking up superbly with Alli and Kane on numerous occasions.
He did have a rare off-day against West Ham in Spurs' last Premier League outing though, with the Hammers digging deep to get a 1-1 draw.