Luciano Spalletti's side heads to the Franz Horr Stadium knowing a place in the next round is within its grasp against the basement boys.
Zenit can reach the Champions League knockout stage for only the second time if it wins at Austria Vienna on Wednesday.
Luciano Spalletti's side currently has 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 it could still qualify with a draw or defeat should its Portuguese rivals fail to beat the Rojiblancos 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 is already destined to finish bottom of the group, but will be eager to end its maiden Champions League campaign on a high by claiming a first victory.
One of its 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.
It then drew at Porto last time out, where Roman Kienast's opener was canceled out by Jackson Martinez.
Zenit has been held to draws in all three of its 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 only 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 has also struggled for victories in recent weeks, with a 2-1 win over Ural on Friday representing its 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.