In the Round 8 match at Sinan Erdem Sports Hall, Zenit were led by Conner Frankamp as the US guard scored 18 points.
Lithuanian forward Mindaugas Kuzminskas racked up 15 points for Zenit.
Jordan Mickey and Billy Baron added 10 points each.
The Turkish club were quite balanced in the scoring section but the 2021 champions lost the clash at home.
Shane Larkin had 14 to lead Anadolu Efes.
German center Tibor Pleiss scored 13 points and French guard Rodrigue Beaubois added 11.
Adrien Moerman and Elijah Bryant scored 10 points apiece.
Anadolu Efes, in 16th place, were handed their sixth loss in the regular season.
They have two wins in the campaign.
Anadolu Efes previously beat Russia's UNICS Kazan in Round 5 and Lithuania's Zalgiris Kaunas in a Round 7 game.
They will visit ALBA Berlin on Nov. 11.
Zenit have a 5-3 record and is in the seventh spot in the EuroLeague standings.
The Russian team previously lost Round 5 and Round 6 games against Spanish powerhouses Barcelona and Real Madrid.
Following the consecutive defeats, Zenit bounced back to earn two straight wins against Bitci Baskonia Vitoria-Gasteiz on Oct. 29 and Anadolu Efes.
In Round 9, Zenit will take on Olympiacos on Nov. 12 in Saint Petersburg.
