The Serie A leaders – and last year’s beaten finalists – thought they had done enough to eliminate Bayern in their own Allianz Arena thanks to first-half goals from Paul Pogba and Juan Cuadrado.
But Robert Lewandowski and Thomas Muller struck after the break to send the game into extra time, and Juve’s race was run when Thiago Alcantara and Kingsley Coman earned Bayern a 4-2 win.
Juve had taken the lead when David Alaba was uncertain when dealing with Sami Khedira’s pass forward and, after goalkeeper Manuel Neuer hesitantly crossed his box to cover, the ball fell to Pogba who found the net.
Juve then added a second when Alvaro Morata fed Cuadrado who dummied Philipp Lahm before smashing home.
Lewandowski dragged Bayern back into the tie on 73 minutes, nodding in Douglas Costa’s cross and Muller forced extra time by heading in on-loan Juve midfielder Coman’s assist.
Substitute Thiago converted Muller’s lay-off to make it 3-2 before, with ten minutes of 120 remaining, Coman hurt his parent club with a close-range coup de grace.