No team has ever progressed after scoring just two goals in the pool stage, but Leonardo Jardim's side would buck that trend with a stalemate at Stade Louis II on Tuesday.
In fact, if Bayer Leverkusen also lose at Benfica, the French outfit would even top the Group C table with that paltry tally - though they will be dumped out if Zenit prevail.
Monaco have claimed two 1-0 wins over the German side, while also drawing 0-0 with Zenit in Russia and against Benfica at home, with their sole defeat being a 1-0 loss in Portugal.
Though their defensive record is impressive, the hosts will hope to make a greater impact at the other end and will be boosted by Dimitar Berbatov having found his scoring boots in Ligue 1 over the last week.
The former Manchester United forward struck from the penalty spot as Monaco beat Lens 2-0 last Tuesday and netted both goals in Friday's win at Toulouse by the same scoreline.
"It's an important victory and one we deserved because we were stronger than Toulouse," Berbatov told the official Ligue 1 website following the latest success.
"We'll head home happy and now we've got another important match coming up, one which could allow us to qualify for the next stage of the Champions League.
"Tuesday's game wasn't in our heads, but we were thinking about it and that's normal. Now the Toulouse match is over and we've won it, we can now start thinking about the next game."
Ricardo Carvalho is suspended for the home team, while highly rated fellow defender Layvin Kurzawa has missed five straight matches with a hamstring injury picked up playing for France.
On a more positive note, Borja Lopez is available again after a long-term knee problem and was an unused substitute versus Toulouse.
Zenit need a victory to advance to the last 16 and will progress as group winners if they win and Bayer Leverkusen lose.
Saturday's 4-0 defeat of FK Krasnodar left them seven points clear at the top of the Russian Premier League, having conceded just once in their last five matches.
"It was very important for us to win because we want to go with this emotion and motivation against Monaco," coach Andre Villas-Boas told the club's official website.
"I'm very proud of the players because the conditions were not very good and they had a fantastic result against a team that is second in the country."
Javi Garcia came off the bench to figure over the weekend after picking up a knock in last month's 1-0 Champions League win over Benfica.
Aleksandr Kerzhakov has been absent since early November, but is back in full training.
