Firstly Juve's Conte and Inter's Morfeo were sent off for fighting, before Christian Vieri equalised in the fourth minute of injury time.
The Turin team now lie fifth in the league, four points behind leaders Inter.
Juve also have a mini injury crisis ahead of Wednesday's game, with Trezeguet, Di Vaio, Tudor, Zambrotta, Pessotto and Del Piero all doubtful with injuries.
Our other Champions League opponents also failed to win, Feyenoord drawing 1-1 at Vitesse Arnhem and slipping to fifth in the league and Kyiv losing 1-0 to Metalurh to slip to fourth in the Ukranian league.
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