A draw would have been good enough for Leonardo Jardim's team to beat their visitors to a place in the knockout phase, but the victory sent them through as Group C winners ahead of Bayer Leverkusen.
Monaco took the game to Zenit after the break, with Abdennour opening the scoring following a free-kick and fellow defender Fabinho breaking forward to complete the win late on.
"We wanted to win this game, even though a draw was enough," Abdennour told UEFA. "A late goal would have sunk us.
"We played offensively. We should always play like that here."
Zenit coach Andre Villas-Boas hailed Monaco's defensive resolve.
"Monaco played very intelligently," said Villas-Boas. "Defensively they are one of the best teams in this competition.
"In the second half they created more space and found ways to win. Congratulations to them."
Villas-Boas singled out Monaco midfielder Joao Moutinho, who was previously under his tutelage at Porto, for special praise.
"Joao Moutinho had a great game both defensively and offensively," said the 37-year-old.
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