Spurs will take two precious away goals into the Champions League last 16 second leg at Wembley next month after Kane’s clinical finish and a clever free-kick from the superb Christian Eriksen ensured a fascinating contest finished level.
Mauricio Pochettino’s men were on the brink after Gonzalo Higuain put Juventus two up within nine minutes, the second a penalty after Ben Davies fouled Federico Bernardeschi.
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.
Juve surrendered all momentum after their blistering start and Spurs will now be targeting a first Champions League quarter-final since 2011.
“It was an excellent performance after that (conceding the two goals) and we deserved to get back into the game,” Kane said after the game.
“We look back now, two away goals we’re taking to Wembley, it’s a great result.
“I had a chance before it (his goal) and I should have scored that, but like I always say, you’ve got to be ready for the next one.
“Dele (Alli) put a great ball in and I managed to finish it off. That got us back into the game, which was important.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.