The Englishman doubled his tally for the afternoon on 59 minutes and while it was the prettiest goal he will score, it was the crucial record-breaker to make him Spurs' most prolific player in the Premier League era.
Crystal Palace's Bakary Sako scored the only goal of the game in the 21st minute as Roy Hodgson's Eagles saw off Burnley 1-0 at Selhurst Park, while West Ham overpowered Huddersfield Town 4-1.
Son delivered an exquisite turn to lose Everton full-back Jonjoe Kenny before driving towards the visitors' goal and putting it on a plate for Kane to tap home.
Kane grabbed Spurs' second goal just after the break as he latched on to Heung-min Son's cross, finishing from close range.
DANIEL LEVY, Spurs chairman, on fending off advances from top European clubs for Harry Kane and Dele Alli, among others.
Everton have already strengthened their attacking ranks this month, with Cenk Tosun arriving from Besiktas to lead the line for Allardyce's men.
Luck is on his side too, with his first goal from Son Heung-min's delivery soon after halftime that put Spurs 2-0 ahead looking fractionally offside. 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. Apart from becoming the club top scorer, Harry Kane owned another record on a historic day as he became the only third player after Thierry Henry and Alan Shearer to have scored 20 or more goals in the English top flight for four continuous seasons.
Iran says no to changes
Iran did not immediately react to the announcement, though officials said they were prepared if Trump had made a decision to act. He paired Friday's concession with other, targeted sanctions on Iran for human rights abuses and ballistic missile development.
He continued: "There are a lot of numbers, but he can do everything because of his mentality and how he is - he is so professional".
Runaway league-leaders City underlined their Premier League dominance by hammering last season's runners-up 4-1 at the Etihad Stadium on December 16, to move 21 points clear of Pochettino's side.
He set a record of 39 Premier League goals in a calendar year in the process and has now joined the former Liverpool captain in the history books.
"Harry can achieve all that he wishes to and all he wants to because it is unbelievable the way he is able to work and his willingness".
But he is not focusing on future milestones, telling BT Sport: "Four-nil in any game is a great result, Everton are a good side and we played well, we created space and took our chances".
Nothing, though, went the way of Everton manager Sam Allardyce, who ended up lambasting his side afterwards.
Everton had emerged early for the second half, but how quickly and brutally they were forced to revert to damage limitation. If it weren't for Jordan Pickford they would have had more today.
He continually powered towards goal whenever he had possession, linking up superbly with Alli and Kane on numerous occasions.