The visitors produced a scintillating display of attacking football and took the lead after nine minutes when Kane curled a shot past Stoke keeper Shay Given.
Title race heats up: Pochettino refuses to write off chasing pack
Christian Eriksen struck the bar for Tottenham before halftime and the visitors wasted several good chances before Eriksen played in Alli to make it 2-0 in the 67th minute.
Alli then somehow struck the post with an empty goal gaping but Kane spared his blushes when he coolly tucked away Erik Lamela's pass for his 24th league goal of the season.
Dier urges Spurs to fight till end
The outstanding Alli completed the rout, volleying in Eriksen's clever chip as Spurs ran riot to inflict Stoke's joint heaviest home defeat in the Premier League.
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