It was 24-year-old Kane's seventh goal in Europe's top club competition this season and puts him level with Steven Gerrard for the most scored by an English player in a single Champions League campaign.
Kane ran onto Dele Alli's through ball, took it round the onrushing Buffon and calmly deposited into an empty net.
Juventus boss Massimiliano Allegri acknowledged his side had blown a great opportunity to establish a foothold in the quarter-final, particularly as Higuain missed a penalty on the stroke of half-time that would have re-established Juventus's two-goal lead.
Despite being one of the stars of the Premier League, Eriksen can go unnoticed at times, particularly given the spotlight commanded by Kane and Alli.
Kane was delighted to take two valuable away goals into the second leg at Wembley, meaning Juventus have to outscore Spurs to win.
Tottenham had a mountain to climb against a side which had reached the Champions League final in two of the past three seasons.
Higuain, Juventus's €90m centre-forward, made a dream start by scoring a stunning second-minute volley before beating Hugo Lloris from the penalty spot seven minutes later.
Champions League: Pochettino says Tottenham will go to Juventus to win
Tottenham are, unequivocally, blessed with one of the most talented, well-rounded starting lineups in the world. THE return leg takes place at Wembley on March 7.
Kane's long-range effort was bundled away by Buffon but the visitors soon won a free kick, which was sacked into the bottom corner by Eriksen via the hand of Buffon who was slow to get down to his right.
"Of course we are more mature".
"We had a lot of chances but with the start in mind, the first nine minutes, we can be very happy with the result in the end", Eriksen said after the match, according to Tottenham.
"I want to congratulate the players - 2-0 down in Turin to a team so hard to break down". Against a team with one of the best defensive records in football and a goalkeeper who had not conceded for 694 minutes until last night, they turned it on once more. "I don't think Juventus minded us having the possession but we had a good balance and won the ball back quickly, and that's what we had to do". We are facing Tottenham in the Champions League, a really physical and technical team.
He told juventus.com: "The second leg in London is still some way off, so now we turn our attentions back to the league and to Sunday's derby against Torino".