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Alli ran onto long pass over the top by Eric Dier and, after instantly controlling the ball, he easily beat stand-in Chelsea keeper Willy Caballero to make it 2-1.
And a series of defensive errors led to the England man making it 3-1 with a simple close-range finish.
Chelsea had led through Alvaro Morata’s header, but Christian Erikssen’s stunning injury-time strike drew Spurs level at the interval.
The Blues started brightly in the second period, but Caballero had to make a stunning save from Son Heung-Min before Alli’s double.
It started well for Chelsea before the break, Morata heading home a fine Victor Moses cross in front of the flapping figure of Tottenham keeper Hugo Lloris after a flowing move started by Antonio Rudiger.
But Eriksen crashed home the equaliser from 25 yards in the first of two minutes of added time.
Marcos Alonso, who scored both goals in the 2-1 win over Tottenham at Wembley in the reverse fixture, also had the ball in the net but appeared marginally offside when he sidefooted home from N’Golo Kante’s far-post cross.
Chelsea looked solid in defence and dangerous on the break with Willian and Eden Hazard a constant threat.
The Brazilian had one tame effort on goal which was blocked on the edge of the area before seeing a deflected strike pushed away by Lloris.
After Morata’s goal, Alonso twice came close to helping the Blues add to the lead with well-struck efforts from a tight angle.
And when Eriksen was gifted possession by Moses, he made the Blues pay for not adding to their lead with a superb hit that deceived Willy Caballero in the air.
It got much worse after the break as Alli showed his class to put Spurs ahead and then made the most of defensive indecision by Andreas Christensen and Cesar Azpilicueta for Tottenham’s third.