In Tottenham's final attack, Winks made a surging run into the area and met an inswinging cross by Georges-Kevin Nkoudou with a stooping header from close range. The win allowed Spurs to trim the gap to first-place Liverpool back to nine points after 23 of 38 games.
Fulham took the lead thanks to an own-goal by Fernando Llorente — the replacement for the injured Kane — in the 17th minute. Alli equalized in the 51st, heading in powerfully from Christian Eriksen's cross, but didn't finish the match.
The England international, an attacking midfielder who can play up front, stayed down clutching the back of his leg after sliding into an advertising hoarding following a tackle. He eventually got up and hobbled to the tunnel.
Kane is out for an estimated two months because of an ankle injury, while Son has joined up with South Korea at the Asian Cup.
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