Hardly for the first time, Heung-Min Son delivered yet another outstanding performance while keeping up a goal record which is none too shabby, either.
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The north Londoners head in to the weekend action sitting fifth in the table - three points off fourth place - but can move level with Liverpool with a win over the Toffees ahead of their clash with Man City on Sunday. "His life is probably fantastic at the moment".
Spurs snatched their deserved lead four minutes later, when Son tapped in for his eighth goal of the season.
Losing 4-0 to Spurs, Everton have now lost eight of their 12 away Premier League games so far this season and have won just once, against Newcastle in December.
Suddenly Tottenham looked risky every time they came forward, and they should have had a third five minutes later when Dele Alli exchanged passes with Son on his way into the box, only to fire his finish into the side-netting with only the keeper to beat.
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The 24-year-old now has 20 Premier League goals this term and 28 in all competitions.
Kane then drew another save from Pickford before the influential Son came within a whisker of deservedly doubling his personal tally when he collected Kane's crossfield pass, cut inside past two defenders and then fired a low strike against the post with the keeper beaten.
More telling than the number of goals is the amount of games in which this venerable record was set: Teddy Sheringham scored 97 goals in 236 appearances; Jermain Defoe scored 91 goals in 276 appearance; Robbie Keane also scored 91 times, his coming in 238 matches; Kane has scored 98 goals in only 135 Premier League matches.
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Everton didn't notch a single shot on goal in the first half, part of a disconcerting trend for the club.