Wayne Rooney thought he had opened the scoring for the Toffees only for his header to be correctly disallowed for offside.
Serge Aurier, Kane, Son and Dele Alli were involved before Christian Eriksen drilled in from 16-yards to provide the cherry on top of a fine performance.
Victory left Spurs level on points with fourth-placed Liverpool, who face runaway Premier League leaders Manchester City today, in a competitive race for a place in next season's Champions League.
The Danish playmaker is the creative fulcrum of the Spurs side and continues to both score and create goals for the silverware-chasing outfit. He took the ball around Jonjoe Kenny before bursting down the left-hand side, with his cross into the box tapped home by a waiting Kane as he equalled Sheringham's record.
James Ward-Prowse scored his first two goals of the Premier League season for Southampton but that wasn't enough to give the Saints a desperately-needed win as hosts Watford rallied to draw 2-2.
"When you look at the number of players who have been brought into this country from overseas - even in the summer - and not worked, particularly up front, it is a risk".
Kane is also only the third player to score at least 20 goals in four consecutive Premier League campaigns after Thierry Henry (five) and Alan Shearer (four).
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. He can achieve all he wishes and he wants", Pochettino told reporters. Recruited for £18m, he has proved a priceless burden-sharer, consistently taking some of the goal pressure off Kane and the creative responsibility from Eriksen, since arriving in 2015.
The forward went into game on 96 goals, one behind Teddy Sheringham, but has now moved ahead of the legendary striker on the list with 98 goals. I should have got back to being a bit more boring and a bit less adventurous.
However, the 25-year-old was keener to pay tribute to Kane. They can cement that with a win at the home of the England senior team, who Allardyce managed for one game but never at Wembley.