French playmaker Nando De Colo led the team from Istanbul to victory at home in the Round 24 game, scoring 24 points with seven assists at Ulker Sports and Event Hall.
Serbian guard Marko Guduric had 19 and Czech center Jan Vesely added 16 for the Turkish club.
US forward Will Thomas led Zenit with 21 points. KC Rivers scored 14. American guard Billy Baron added 13.
Fenerbahce Beko have 14 wins in the 2020-21 EuroLeague regular season.
This season Zenit has lost 9 matches.
The Russian team suffered their third straight loss.
Fenerbahce Beko will next play Germany's ALBA Berlin in Istanbul on Feb. 19.
