Max Allegri's side dug themselves out of a hole to remain alive in the Champions League Round of 16 tie despite conceding two away goals to Pep Guardiola's German giants.
Thomas Muller opened the scoring late in the first half when he side-footed home from about 10 yards after Douglas Costa's aerial cut-back from Arjen Robben's light-footed cross had been deflected into his path by Andrea Barzagli.
Bayern quickly added a second 10 minutes after the re-start when Robben received a pass from Robert Lewandowski on the right side of the area, before cutting back and feigning to shoot prior to a lovely curling effort which left Gigi Buffon with no chance.
However, the Bianconeri fought back eight minutes through Paulo Dybala who was on the end of a deft little pass from Mario Mandzukic and finished with aplomb beyond Manuel Neuer for his very first goal in this competition.
On 76 minutes, Juve equalised when Mandzukic found Alvaro Morata on the left side of the area allowing the Spaniard to head into the path of an onrushing Stefano Sturaro who half-volleyed beyond Neuer from pointblank range.
Earlier in the contest, Arturo Vidal stung the palms of former teammate Buffon with a piledriver from range before Muller got it completely wrong when failing to control Lewandowski's short pass on the edge of the six-yard box, forcing him to miss what should have been a certain goal.
Late in the first half, Juventus had big shouts for a penalty when Vidal clattered into the back of Dybala when cleaning the ball but referee Martin Atkinson waved away the protests.
In the 67th minute, with the score at 2-1, Mandzukic found Juan Cuadrado unmarked in the area but the Colombian winger saw his well-struck effort saved by Neuer before Paul Pogba saw his attempt curl over from the edge of the box.
Juventus chased a third goal at the death with Pogba heading over late before Neuer safely held a long range effort to keep it at 2-2.
It sets up a tantalising return leg in at the Allianz Arena on Munich on March 16 with Bayern holding the advantage thanks to their two goals on the road.
2015/16 UEFA Champions League - Round of 16 first leg