Deciding goal came thanks to Francisco Conceicao's 83rd-minute winner, making it two wins from two matches in the Champions League for his team.
Juve, who were reduced to 10 when keeper Michele Di Gregorio was sent off on the hour for a handball outside the box, fell 1-0 down in the 30th minute when Benjamin Sesko drilled in off the crossbar.
The Italians, who had suffered a double blow at the start of the game with the injuries to captain Bremer and Nicolas Gonzalez, recovered after the break.
They levelled through Dusan Vlahovic in the 50th minute but went 2-1 down when Sesko converted a penalty in the 65th to put the hosts back in front.
Serbia striker Vlahovic came to their rescue again three minutes later, curling a left-footed shot into the far top corner to equalise before Conceicao's fine finish completed their comeback.