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The team initially fell just short of the points required but the title was sealed when Ferrari's Kimi Raikkonen was demoted from fifth to eighth.
The Finn was given a 30-second penalty for causing a last-lap collision with Williams driver Valtteri Bottas.
That saw Mercedes seal the championship with four races still to go.
Mercedes also clinched the title in Russia last year. Although there were three races to go in 2014, it is effectively the same stage of the season because double points were awarded at the final race of last year.
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The triumph confirms Mercedes' domination of the turbo hybrid engine formula that was introduced into F1 in 2014.
The team have lost only six of the 34 races that have been held since the start of the 2014 season.
Hamilton's victory means he can seal a second consecutive drivers' title at the next race in Austin, Texas on 25 October, if he out-scores Ferrari's Sebastian Vettel by nine points and his Mercedes team-mate Nico Rosberg by two in the US.
Full race results
Mercedes have won their second consecutive constructors' title following Lewis Hamilton's victory in the Russian Grand Prix.