Luciano Spalletti's side currently have the edge over Porto in the race for second spot behind Atletico Madrid in Group G.
Victory in the Austrian capital would guarantee Zenit's progression, while they could progress with a draw or defeat should Porto fail to beat Atletico in Spain.
Zenit previously made it through the group stage in the 2011-12 season before bowing out to Benfica in the round of 16.
Vienna are already guaranteed to finish bottom of the group, but will be keen to end their maiden Champions League campaign on a high by claiming a first victory.
One of their two points to date was collected at Zenit on October 1 in a goalless draw that saw Axel Witsel sent off for the hosts.
In avoiding defeat at the Petrovsky Stadium, Vienna claimed the first point by an Austrian side in the Champions League since Sturm Graz defeated Panathinaikos in 2001.
They then managed another draw at Porto last time out, where Roman Kienast's opener was cancelled out by Jackson Martinez.
Zenit have been held to draws in all three of their home group-stage fixtures this season, but remain on course to qualify having won away at Porto on matchday three.
The Russian club can take confidence from Vienna's dismal recent form, which has seen Nenad Bjelica's men win just four of 15 matches across all competitions.
Struggling Admira Wacker Modling held the reigning Austrian Bundesliga champions to a 2-2 draw on Saturday.
However, Zenit have also struggled for victories in recent weeks, with a 2-1 win over Ural on Friday representing their first success in eight games.
Vienna could hand a start to Marko Stankovic, who has made two substitute appearances since spending six weeks on the sidelines with a muscular problem.
Anatoliy Tymoshchuk could make his 50th Champions League appearance, having represented Bayern Munich and Shakhtar Donetsk prior to linking up with Zenit.
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