The Russians, third in the group six points behind leaders Juventus and two adrift of Real Madrid, must beat the Italians at home and the Spanish champions in Madrid on December 10 to join Juve in the last 16.
Zenit beat Spartak Moscow 3-1 on Saturday but by finishing fifth in the Russian league they are outside the Champions League places for next season.
"Obviously, finishing fifth is a big disappointment for both the club and our fans," said their Dutch coach Dick Advocaat, who steered Zenit to their first Russian title in almost a quarter of a century last year and UEFA Cup victory in May.
"It has been a very long a tough season. Now we have only two games left and we want to end the year on a high note."
Zenit have a full squad available for Tuesday except for French defender Sebastien Puygrenier, who is serving a one-match ban after being sent off against BATE Borisov three weeks ago.
Russia playmaker Andrei Arshavin has an added incentive to excel against Juventus and Real after demanding a move away from St Petersburg in the off season.
JUVE THROUGH
Juventus, who reached the last 16 after winning 2-0 at Real Madrid last time out, lost 1-0 at Serie A leaders Inter Milan on Saturday.
Claudio Ranieri's side barely had a shot at goal as a run of seven straight wins in all competitions came to an end.
"We wanted to win to keep the title race tight but it doesn't change our objectives. We want to improve on the third place we managed last season in the championship and go as far as possible in Champions League," Ranieri told reporters.
Juve lost Tiago to a knee injury in the fourth minute and the Portuguese midfielder is now highly doubtful and Dane Christian Poulsen is also struggling for fitness.
Ranieri is expected to rest some players but finishing top of the group remains an aim.
Alessandro Del Piero, 34, scored both goals against Real but has netted just once since and could be given a break, in which case Vincenzo Iaquinta will come into the side.
Goalkeeper Gianluigi Buffon remains sidelined with a leg injury.
Probable teams:
Zenit St Petersburg: 16-Vyacheslav Malafeyev; 22-Alexander Anyukov, 4-Ivica Krizanac, 11-Radek Sirl, 15-Roman Shirokov; 18-Konstantin Zyryanov, 19-Danny, 27-Igor Denisov, 44-Anatoliy Tymoshchuk; 8-Pavel Pogrebnyak, 10-Andrei Arshavin
Juventus: 13-Alex Manninger; 21-Zdenek Grygera, 4-Olof Mellberg, 33-Nicola Legrottaglie, 29-Paolo De Ceglie; 16-Mauro Camoranesi, 19-Claudio Marchisio, 11-Pavel Nedved, 20-Sebastian Giovinco; 9-Vincenzo Iaquinta, 8-Amauri
Referee: Claus Bo Larsen (Denmark)
