Milan have already qualified for the knockout stages behind leaders Malaga but there is the matter of pride at stake for the Italians, while Zenit know they need a good result to secure their place in the Europa League.
Zenit are third in the group, tied on points with Anderlecht but ahead on goal difference, and need a better result than the Belgian champions who take on Malaga, to ensure their progress.
For Allegri, a home win would finish off the group stages in style following two draws to date against Malaga and Anderlecht, and the Milan coach confirmed he would not change his game plan for the match.
"We must win," Allegri told www.gazzetta.it. "In matches where we had already qualified, AC Milan did almost never did well.
"It is going to be a game in order to extend the streak of results. Winning is good.
"Winning helps to stay calm and we must also prepare for the championship race. It is not a race you need to qualify, but if you do not get a positive result it is only two or three days to reconsider and we do not have that time."
However, Allegri could make some changes with Stephan El Shaarawy one who could be rested while Mathieu Flamini and Massimo Ambrosini could come into the midfield in place of Nigel de Jong and Riccardo Montolivo.
Zenit are looking for a Europa League place but Italian coach Luciano Spalletti will be without striker Aleksandr Kerzjakov due to a thigh injury while Vladimir Bystrov is suspended after he was shown a red card against Malaga.
Brazil international Hulk looks set to lead the forward line with Aleksandr Bukharov, and should take confidence from last weekend's 4-2 win over Spartak Moscow where he scored the opening goal before being substituted in the second half.