In this way he will break all the records in the Premier League.
Kane scored his brace from close range in the second half, to take his tally to 98 league goals in just 135 appearances.
Harry Kane needs two more goals to reach his Premier League century.
In a unusual game that ebbed and flowed, Wayne Rooney had the first chance after a quiet opening, with the striker latching onto a long kick from Jordan Pickford and dragging a left-footed shot wide of the right post from inside the area on 16 minutes.
Gylfi Sigurdsson's corner was flicked on by debutant Cenk Tosun, finding the head of Wayne Rooney, and although his glancing effort beat Hugo Lloris, the linesman already had his flag raised.
Tottenham will be without midfielder Harry Winks as he's still working his way back from an ankle injury while Toby Alderweireld is also still nursing a hamstring problem.
Elsewhere, Alan Pardew oversaw his first Premier League victory as West Bromich Albion manager thanks to a 2-0 win over Brighton and Hove Albion, while Rafael Benitez's Newcastle United came from behind to draw 1-1 with bottom-of-the-table Swansea City.
Yet Everton's hopes of reeling in Tottenham lay in tatters two minutes after the restart.
Spurs snatched their deserved lead four minutes later, when Son tapped in for his eighth goal of the season. 'Hopefully his ability and goalscoring ability will help us along the way, but we've got to get back to the basics defensively like I did when I first started'.
Kane then took over, tapping home a Son centre before he scored a scruffy second after some poor Everton defending following an Eric Dier cross.
"Of course, the chairman is the man who manages everything and in the end takes all the decisions", Pochettino said ahead of Tottenham's Premier League match against Everton on Saturday.