The Brit claimed his ninth win of the year and fourth on the bounce over his Mercedes rival.
Rosberg’s second place after recovering from a first-lap mistake secured the constructors’ title for their team.
The German is now 17 points adrift of Hamilton with a maximum of 100 points left to drive for this season.
Celebrations were again subdued though, with the entire grid worried for Marussia driver Jules Bianchi, who remains in a critical condition after crashing in Japan.
His fellow drivers and his team paid touching tributes to the Frenchman, but his team-mate Max Chilton was forced to retired after nine laps.
Russian president Putin attended the race having been instrumental in it coming to Russia. He also appeared on the podium at the end of the race to present the honours to Hamilton and Mercedes.
“Nico did a great job to recover,” Hamilton said. “The car was performing really well. It’s history for us. I feel very proud to be a part of it. To get the first constructors’ championship for Mercedes-Benz is a wonderful day.”
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