England striker Kane took his Spurs total in the competition to 98, leaving him one clear of White Hart Lane legend Teddy Sheringham. In doing so, Son joined Jermain Defoe as the only Tottenham player to score a goal in five consecutive home matches.
The England global stole the headlines once again as Spurs drew level on points with fourth-placed Liverpool, overtaking club legend Teddy Sheringham to stand out on his own as Tottenham's most prolific player of the Premier League era.
'But for Jordan Pickford they could have had more, so I'm hugely disappointed in the professionalism of my players today.
Constantly pressing on the defenders, Tosun was a handful but does need to slightly curb his enthusiasm as he could receive silly cautions throughout his Everton career.
'I think it's really out of order that you relinquish that responsibility just cos you've gone 2-0 down one minute into the second half... there's still another 44 minutes plus injury time to play, and play your way back into the game like you did in the first half'.
Son Heung-Min (Tottenham).
That means Kane will not be leaving and Spurs will fend off bids for the likes of Alli, Eriksen, Danny Rosem Toby Alderweireld etc. Continued his fine form with another home goal and an assist to cap a lively, industrious display.
Kane scored eight league goals in December, including a brace against Stoke and hat tricks in wins against Burnley and Southampton, to break Alan Shearer's Premier League record for goals in a calendar year (39) and overtake Barcelona's Lionel Messi for the most goals for club and country by any player in Europe's major leagues in 2017 (56).
Tosun was put out of his misery just after the hour and was replaced by Dominc Calvert-Lewin yet this was an extremely unsatisfactory match for Allardyce.
Everton didn't notch a single shot on goal in the first half, part of a disconcerting trend for the club.
But that arrived soon enough and in superbly stylish fashion as Serge Aurier, Son and Alli combined beautifully to open up the chance for Eriksen to smash home.
47' - GOAL! Tottenham 2-0 Everton.
The South Korean global charged down the left flank and in a manner similar to the first goal, he dragged his shot into the box with Kane tapping the ball into the net.
59' - GOAL! Tottenham 3-0 Everton. More slick play from Spurs. Alli meets the rebound but can only steer straight at the keeper.