Sergey Semak’s side now have an unassailable 13-point lead over second-placed Lokomotiv Moscow with four rounds to go.
Zenit’ seventh top-flight title came after last season’s victory where they also pipped the side from the capital city.
League top-goal scorer Artem Dzyuba on 17 and Sardar Azmoun, who trails his team-mate with his tally of 15, both added to their accounts at Krasnodar despite Daniil Utkin’s double for the hosts.
Zenit can add to their trophy haul with a Russian Cup semi-final against Spartak Moscow scheduled for July 18.
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