However, Son accepts trying to match Kane is a futile task.
Subs used: Wanyama (5), Sissoko (n/a), Lamela (n/a).
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.
Man of the match: Heung-Min Son.
Southampton drew 2-2 at Watford after taking a 2-0 lead but Abdoulaye Doucoure sent the ball into the net with his right hand to score Watford's equaliser in the 90th minute.
It is easy to expect more goals from Kane today at odds of 2-1 to be the first scorer.
Tottenham made one change with Mousa Dembele replacing Moussa Sissoko.
The Toffees opted for the long ball on numerous occasions as they looked to use the height of new signing Cenk Tosun.
Son's tap-in steadied Tottenham, though Everton continued to press.
Kane's goals have come in only 135 games, while Sheringham took 237.
Kane has now scored 20 league goals this season, three more than the next most prolific, Liverpool's Mohamed Salah.
With Everton's defence in tatters, Eriksen completed the rout by collecting fellow midfielder Dele Alli's clever flick on before beating Everton goalkeeper Jordan Pickford with a crisp finish in the 81st minute.
"West Brom becomes a massive game next week so we don't get dragged back into that relegation zone".
Yet Everton's hopes of reeling in Tottenham lay in tatters two minutes after the restart.
The second effort took Kane onto 98 Premier League goals for Tottenham - putting him past Teddy Sheringham and making him the club's record goalscorer in the league format which started in 1992. "With his mentality and his professionalism he can achieve all that he wishes. He is always thinking to try to improve, improve, improve, score goals and improve for the team".
"Maybe I have to take the responsibility for playing too many attack-minded players".
"It shocked me. I've not seen it since I got here but I've seen it now, and it's probably what was apparent before I got here".
But he loves facing the men from Goodison Park and has scored four goals in his last two appearances against them.
He continually powered towards goal whenever he had possession, linking up superbly with Alli and Kane on numerous occasions.
Son has been a key figure for Mauricio Pochettino's side, with this season and last more than showing as to why Tottenham signed him from Bayer Leverkusen.