But Higuain came within a whisker of putting the tie out of sight on the half-hour after a lightning Juventus break.
It was not in the same stratosphere as Roy Keane's performance in Turin for Manchester United against Juventus in 1999, nor was it comparable to Steven Gerrard's enormous display of leadership six years later, which brought Liverpool back from the dead to win the Champions League against AC Milan in Istanbul. Seven minutes later it was 2-0 after Ben Davies gave away a penalty with a reckless challenge on Federico Bernardeschi. "For 83 minutes we dominated Juventus and that is a thing to praise".
Higuain took the ball but rather than celebrate a first-half hat-trick his penalty kick rattled against the crossbar.
But Kane pulled one back, only Juve's second goal conceded in 17 games, before Higuain missed a second penalty, in what could prove a decisive moment in this tie. Higuain's first came after 73.
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.
By the end of the contest, the hosts found themselves scrambling to preserve the draw.
Spurs are still undefeated in Europe this season, a record that was in severe jeopardy when Juventus scored two goals in the opening nine minutes at The Allianz Stadium.
"I think people have lost a bit of objectivity", said Allegri.
"I feel so proud", Tottenham coach Mauricio Pochettino said.
"He's a player who links the team and he was fantastic".
Juventus defender Mattia De Sciglio admits his side "wasted" a big opportunity against Tottenham as they let a 2-0 lead slip to draw 2-2 in Turin, but remains confident that they can earn a win in London.
"That drives me nuts, because people don't have an idea about the other teams".
Having looked as though they were heading for a potentially decisive first-leg defeat, Spurs fought back to overcome the experience of Juve and claim the draw that leaves next month's return game at Wembley perfectly poised.