Juve made a dream start with the opening strike from Gonzalo Higuain, who got in a perfect position to volley in Miralem Pjanic’s free-kick in the second minute.
It got better for them after the Argentine stepped up to complete his brace from the spot inside the opening 10 minutes after Ben Davies fouled Pjanic.
That was the fastest a Juventus player managed to get a double in the competition’s history, and after turning defence to attack, Higuain fired inches away from his hat-trick later on.
It took the visitors 25 minutes to get their first attempt at goal when Harry Kane got the best out of Gianluigi Buffon with a header from Christian Eriksen’s cross.
On the half and hour mark, Kane turned from his marker and got left side off goal to force Buffon to a fingertip block.
It was third time lucky for Kane after he got ahead of the last defender before beating the offside trap for a simple tap-in five minutes later after drawing Buffon out wide.
With their tails up, Spurs kept up the pressure and Buffon had to come up with another block after Eriksen shot from the edge of the area which the former punched back into play.
After sustaining the onslaught, the Old Lady got another lifeline to regain their two-goal deficit with another penalty after Serge Aurier clipped Douglas Costa in the box.
Higuain stepped forward hoping to complete his treble, but he struck the top of the crossbar after trying to go down the middle as the half ended 2-1.
Hugo Lloris made a vital save 12 minutes in the second half off Federico Bernardeschi, who cut inside from the right before providing the visitors with a scary moment.