Andre Villas-Boas has made a perfect start to life in Russia, with Saturday's victory Zenit's fourth in as many matches under the Portuguese coach.
Hulk put them ahead in the 21st minute, but the visitors were level seven minutes after the interval through Joaozinho.
Anzhi remain rooted to the foot of the table, two points behind Volga, who were thumped 5-0 at home by Dinamo Moscow on Monday.
Ahmed Musa's 17th-minute strike was enough to earn them a 1-0 win over Ural, who are still stuck in the bottom four.
Spartak were also 1-0 winners, with Yura Movsisyan's early goal proving the difference in their home clash against Krylya Sovetov.
At the wrong end of the table, Tom Tomsk's 0-0 draw with Amkar Perm did little to ease their relegation fears, while Terek Grozny's recent good run of form continued at home to Rostov.
Mauricio gave them the lead from the penalty spot in the 26th minute and Rostov's Guelor Kanga was sent off nine minutes later.
Ailton Almeida then added a pair of goals, the second of which was a penalty, meaning Rizvan Utsiev's second yellow card had little impact on the match.
