Hardly for the first time, Heung-Min Son delivered yet another outstanding performance while keeping up a goal record which is none too shabby, either.
Spurs doubled their lead two minutes into the second half as Son turned provider to pick out Kane, who made no mistake from close range, 2-0.
Tottenham is now level on points with fourth-placed Liverpool and only three behind Chelsea, the defending championhaving been held to a 0-0 draw by Leicester City that denied it the chance to move above Manchester United in second.
While Sam Allardyce did his utmost, through mind-numbingly tiresome defensive tactics, to stifle and frustrate Tottenham, Mauricio Pochettino's men were up to the test. Totenham's fist good chance fell in the 15th minute to Son, whose flicked header from a Christian Eriksen free kick delivery skimmed inches over the crossbar.
"I thought we had cut that out, so for me it is about making the players understand that it has happened once, in the second half - it can not happen again". Five players were involved in the build-up, but it was a superb back heel from Alli at the edge of the box that found Eriksen on the left, before he powered home to seal a superb Spurs victory.
Tottenham Hotspur won 4-0 against Everton in the Premier League clash on Saturday.
It was Kane's 98th goal for Spurs in the Premier League making him the club's all time top scorer in the competition.
Tottenham has no such problems with Kane.
However, Everton were managed by Ronald Koeman for that fixture and things have since improved under the guidance of Sam Allardyce, with the Toffees putting together an unbeaten run in his first seven games in charge. "I'm so happy because for us it was a game that we must win, a massive three points for us today".
Hugo Lloris celebrates 74' - Victor Wanyama replaces Eric Dier for Spurs.
"I think we played very well, it's not just me because the team-mates help me that's why I score a lot of goals at Wembley", he said.