The home side had the better chances overall but were hurt by the sending off of Alex Witsel just before half-time and could not find the breakthrough.
The result is a blow to Zenit's hopes of making it out of Group G, with Atletico Madrid and Porto still to visit the Stadion Petrovski.
Vienna went into the match in poor form and in the midst of an injury crisis, and they were almost behind in the 12th minute.
Hulk unleashed a shot from the edge of the area that was misjudged by goalkeeper Heinz Lindner, who scrambled it against a post.
The visitors reacted well and from a counter-attack two minutes later Daniel Royer forced Yuri Lodygin into a diving save, with Philipp Hosiner unable to seize on the rebound.
Hulk looked the man most likely to score for the Russian league leaders and Lindner did well to push the ball behind for a corner when the Brazilian produced a powerful shot on the turn from the centre of the box.
Linder looked beaten in the 27th minute when Nicolas Lombaerts headed towards goal but Christian Ramsebner cleared the danger.
Moments later Ramsebner was in action at the other end when Lodygin came flying out of goal to clear a corner but the Vienna man's effort was blocked by Danny.
The hosts continued to look the more threatening and in the 33rd minute Hulk and Aleksandr Kerzhakov broke towards goal but the latter sliced his shot wide when he should have done much better.
Eight minutes later it was Vienna's turn to hit the woodwork as Hosiner drove at the Zenit defence after they had given the ball away and his low shot clipped a post.
A minute before half-time the hosts were reduced to 10 men when Witsel was shown a straight red card for a sliding challenge on Florian Mader in what appeared a very harsh decision.
The numerical deficit did not stop Zenit threatening the Vienna goal in the second half, but neither they nor the Austrians could find a breakthrough.
Lindner saved from Danny in the 55th minute while Hulk's last effort was a late free-kick that was straight at the keeper.
Vienna struggled to turn promising positions into chances, with Mader and Thomas Murg both shooting off target.