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Zenit started the match on the front foot and were within inches of going ahead in the 12th minute when Hulk unleashed a shot from the edge of the area that Vienna goalkeeper Heinz Lindner tipped onto the post.
Minutes later and it was Lindner who came out on top against Hulk once more, beating away the Brazilian's close-range effort.
Soon after the half-hour mark, the hosts squandered another chance when Aleksandr Kerzhakov fired high and wide.
The second period was a bitty affair where Hulk again was the closest to breaking the deadlock, but his 73rd-minute free kick whizzed past the post.
A draw sees both sides pick up their first points of this season's competition.