With the Italian side already through, the match was more critical for the hosts who failed to snatch a victory.
Both teams had a plenty of opportunities throughout the game, but none were converted.
The home side, who were in desperate need of a victory to revive their qualification hopes, started off the match with a consistent onslaught, looking for an early opener.
Their opponents, on the other hand, were more dangerous on the counter attack.
Claudio Ranieri's men were close to taking the lead on 19 minutes, when Olof Mellberg's free-kick was denied by the right post.
Ironically, the same woodwork denied Vincenzo Iaquinta's tame shot ten minutes later.
Zenit tightened their grip late in the first half and became more threatening upfront, but Alexander Manninger shined to prevent them from breaking the deadlock.
After the interval, Juventus took the upper hand, and skipper Alessandro Del Piero could have broken the deadlock on 56 minutes when he volleyed Zdenek Grygera's cross, but Vyacheslav Malafeev saved it.
In the dying minutes, the hosts intensified their attacks, trying to net a last-gasp winner but to no avail.
Elsewhere, Real Madrid booked a place in the next round after registering a much-needed 1-0 victory over minnows BATE Borisov, thanks to Raul Gonzalez's winner.
Los Merengues captain cannoned home after latching on to Royston Drenthe's low cross on seven minutes.
The Spanish champions, who have been suffering a stuttering form for quite a while, secured the second place with nine points, trailing Juventus by two.