The Blues were looking to set a new top-flight record of 14 successive league wins in one season but they were denied by Mauricio Pochettino’s men, who have moved up to third following their victory.
Alli, who netted two strikes apiece against Southampton and Watford in Spurs’ previous two league outings, continued his rich vein of goalscoring form with a header in added time at the end of the first half.
And the England international soon added his second as he ghosted into the Chelsea box to head past Thibaut Courtois after 54 minutes.
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