The England international went down under a tackle from Alex Sandro and was withdrawn before the break, potentially leaving a sizeable hole at right-back after the sale of Kyle Walker to Manchester City.
Despite the setback, Spurs will take plenty of positives from securing a third pre-season victory in a match they largely controlled.
Juve, meanwhile, produced occasional glimpses without ever showing the quality that made them UEFA Champions League finalists last term.
Only a superb second-half save from Gianluigi Buffon prevented a heavier margin of victory after Kane and Eriksen scored either side of half-time with a pair of well-taken goals.
Trippier first received attention after getting his leg caught in the turf inside the opening five minutes, although the 26-year-old soon returned to spectacular effect.
Overlapping on the right, he received Moussa Sissoko's pass and delivered a delightful dinked cross for Kane to nod in at the back post.
Juve settled and Paulo Dybala harmlessly guided his side's first attempt over the bar, before Gonzalo Higuain drew a sharp save from Hugo Lloris at close range.
Kane then wasted a clear chance for a second when Buffon's heavy touch created panic but, after Eriksen turned the ball back into the area, the England striker sidefooted his finish straight at the veteran keeper with the goal gaping.
Sissoko went even closer soon afterwards when he was afforded time to size up a shot inside the area, only to see his curling effort come back off the post.
Tottenham's impressive half ended on a sour note with Trippier succumbing to his earlier knock and being forced from the pitch.
The Premier League side began the second period in far brighter fashion as Dele Alli slipped Eriksen in behind to make it 2-0 in the 52nd minute, the Denmark international rounding Buffon and applying a simple finish.
It would have been three had Buffon's fingertips not pushed a Kane drive against the crossbar while Lloris was called upon to tip a Dybala effort around the post.
Massimiliano Allegri made several changes from half-time onwards, introducing the likes of Federico Bernardeschi and Claudio Marchisio, but it was young striker Moise Kean who turned their best chance of the match against the woodwork from point-blank range.
Both sides now await their first competitive matches next weekend as Juve meet Lazio in the Supercoppa Italiana while Spurs travel to Newcastle United for their Premier League opener.