Hamilton's closest rival and team mate Valtteri Bottas took second place, with Hamilton also banking an extra point for the fastest lap.
Ferrari's Charles Leclerc finished third after an early team orders controversy with Sebastian Vettel, whose retirement on the 28th of 53 laps brought out a safety car that cemented Hamilton's lead.
Ferrari had won the previous three races but Mercedes retained their unbeaten record in Russia dating back to the first race in Sochi in 2014. The victory was the 82nd of Hamilton's career and ninth of the season.
