The Bianconeri weighed in with several decent chances and finished the game strongly, but the hosts had an inspired Hugo Lloris to thank for several impressive saves.
The defender was felled by the Brazilian left-back after just four minutes, which led to a lengthy break as he was treated on the pitch, but it looked like the worst was over as he got up and continued.
Six minutes later, he whipped in a pinpoint cross from the touchline which floated beautifully into the path of Kane, who nodded home past Gianluigi Buffon to give Spurs the lead.
In particular, Lloris had to be at his best to keep out a point-blank chance from Higuain following a corner.
However, Mauricio Pochettino's charges were dominant in all departments and could have been several goals to the good had Kane not fluffed two great chances in quick succession and Moussa Sissoko been luckier with an effort that struck the post.
Unfortunately for Spurs and Trippier, the right-back injured himself in another challenge with Sandro shortly before the break, and he could not continue, Kyle Walker-Peters taking his place on the pitch.
For all their wasted efforts, Spurs managed to double the lead early on after the restart, Alli unlocking the Juve defence with a through-ball that found Eriksen, who in turn rounded Buffon and slotted home into an empty net.
Massimiliano Allegri's charges did not let their heads drop and enjoyed their most dominant spell late on in the game, but Lloris kept out efforts from Dybala and Juan Cuadrado, while Federico Bernardeschi fired wide and Moise Kean rattled the woodwork.
Ultimately, Spurs were able to see the game out and record an impressive win against the Serie A champions and Champions League finalists ahead of the start of the new Premier League season, which sees them open their account at Newcastle United.