Kane bagged a brace against Everton to put his side on the front seat after Korean ace Son Heung-Min opened the scoring in the first half.
The South Korea worldwide was involved again as Kane netted his first of the game two minutes after the restart.
They added a fourth goal with nine minutes remaining when Christian Eriksen rounded off an excellent attacking move from the London club. In the process he took his tally against Everton to four this season, helping his team move level with Liverpool in fourth place and combining brilliantly with the waspish Son Heung-min.
But with 26 minutes gone, Son timed everything right when Serge Aurier's scuffed shot fizzed across the box and he steered the ball home from close range.
"It was a shock second-half performance".
Harry Kane admitted he might have been offside for the first of the two goals which made him Tottenham's top scorer of the Premier League era on Saturday. 89' - Wayne Rooney crosses for Dominic Calvert-Lewin but Jan Vertonghen gets just enough on the ball to divert it away from the Everton substitute.
"West Brom becomes a massive game next week so we don't get dragged back into that relegation zone".
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.
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Saturday's late kick-off saw England forward Kane score his 98th Premier League goal and surpass Teddy Sheringham's previous club record of 97.
Emre Belozoglu only started five Premier League matches during the Sam Allardyce short-lived (but still far too long) era at Newcastle and doesn't have anything good to say about his former boss.
Yet Everton's hopes of reeling in Tottenham lay in tatters two minutes after the restart.
The Tottenham striker scored eight goals in six matches, including back-to-back hat-tricks against Burnley and Southampton in a vintage month.
"When the second goal went in and if it was offside it was a killer, but that doesn't allow us to throw the towel in and relinquish that defensive responsibility".
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.
"I thought he was good and he's experienced a hard game, and there won't be many more hard ones to play away from home than against Tottenham" Allardyce said.