An early double from Gonzalo Higuain appeared to have set the Serie A champions up for a comfortable victory, before Harry Kane and Christian Eriksen gave Spurs a slight advantage to take back to Wembley with two away goals.
Juve, unbeaten at home in the competition since losing to Bayern Munich in April 2013, took the lead inside the first two minutes through a fine volley from Higuain, although he was perhaps lucky not to be penalised for offside.
The Argentina striker made it 2-0 in the ninth minute from the penalty spot, but Spurs – buoyed by their weekend win over fierce rivals Arsenal – began to take control from then on and Kane's 33rd goal of the season, the first conceded by Gianluigi Buffon in 694 minutes for club and country, gave Spurs a lifeline.
Higuain missed a second penalty before the break during an uncharacteristically nervous performance from Massimiliano Allegri's side, and Spurs secured a fine result 19 minutes from time, when Eriksen wrong-footed Buffon with a free-kick.
The result ends Juve's 11-game winning run in all competitions and leaves them facing a sizeable task if they are to keep their quest alive for a third final appearance in four years.
2016 - It's the first time since February 2016 that Juventus concede at least 2 goals in a CL game at home (2-2 v Bayern). Danger. pic.twitter.com/K3hHUxa66b— OptaJean (@OptaJean) February 13, 2018
Juve's lightning start saw them take the lead with their fastest goal in a Champions League match since Alessandro Del Piero scored against Manchester United in 1997 inside 30 seconds.
Miralem Pjanic won a free-kick against Mousa Dembele and clipped the ball cleverly into the path of Higuain, who watched the ball drop over his shoulder before volleying across Hugo Lloris' goal and into the bottom-left corner.
Matters got worse for Spurs just six minutes later. Ben Davies felled Federico Bernardeschi inside the penalty area and Higuain swept low past Lloris from the spot, despite the France keeper again getting a glove to the ball.
2 - Gonzalo Higuain's brace is the fastest scored by a Juventus player in Champions League/European Cup history. Sprint. #JUVTOT— OptaPaolo (@OptaPaolo) February 13, 2018
Kane felt aggrieved not to win a spot-kick of his own after going down under pressure from Medhi Benatia, and the England striker wasted a glorious chance to get a goal back 26 minutes in, heading straight at Buffon from point-blank range.
But Kane gave the visitors hope with 35 minutes played, racing onto Dele Alli's pass before beating the onrushing Buffon and firing home.
7 - Harry Kane has equalled the record for the most goals scored by an English player in a single Champions League season (7), level with Steven Gerrard in 2008-09. Comeback. pic.twitter.com/NRIrtXw0Zi— OptaJoe (@OptaJoe) February 13, 2018
Spurs were in the ascendancy, but Juve spurned the chance to make it 3-1 seconds before half-time, when Higuain blasted his second penalty of the game off the crossbar after Serge Aurier had brought down Douglas Costa.
The second half was a much more balanced and less open affair, with Juve coming closest to the critical fourth goal in the tie when Bernardeschi's drive was tipped past the post by Lloris.
Mauricio Pochettino's side were still the more composed of the two teams, though, and they got the second goal their performance deserved with 71 minutes played, as Eriksen fizzed a free-kick into the bottom-left corner past the uncertain Buffon, setting up a tantalising second leg on March 7.
Key Opta facts:
- Juventus are unbeaten in their last six Champions League home games against English sides (W2 D4) – with their last loss coming against Manchester United in February 2003.
- The Serie A side failed to win a Champions League home game after being two or more goals ahead for the just the second time and the first time since April 1999 – losing 3-2 to Man United after being 2-0 up in the opening 11 minutes (semi-final second leg).
- In fact, Tottenham are the first team to overturn a two-goal deficit at the Allianz Stadium since Juve moved there in 2011.
- Prior to Harry Kane's goal, Gianluigi Buffon had not conceded for 694 minutes for Juventus and Italy.
- Spurs are the first team to concede two first-half penalties in the Champions League knockout stages since Milan in April 2012 versus Barcelona.