The Briton set a track record time of one minute 33.067 seconds, with Finnish team mate Valtteri Bottas - last year's winner - second fastest.
Ferrari's German contender Sebastian Vettel, 40 points adrift of Hamilton with six races remaining and his hopes of a fifth title receding fast, was third on the timesheets but 0.600 off the pace.
The Italian team also raised eyebrows by sending Vettel out just as the session was ending for a practice start, forcing him to stop at the pitlane exit when the light showed red.
Team mate Kimi Raikkonen was also ordered to stop as he was about to depart the garage.
Mercedes have yet to be beaten in Sochi, a track that has historically seen little overtaking and that made its debut on the calendar in 2014 after the Winter Olympics in the Black Sea resort.
Hamilton, a two times winner in Sochi, was also quickest on Friday when Ferrari appeared to be struggling and looks a good bet to stretch his lead on Sunday with Mercedes bringing upgrades to their car.
Raikkonen was fourth, ahead of the Red Bulls of Max Verstappen and Daniel Ricciardo who both have grid penalties and will start at the back.
Sauber's Charles Leclerc, the young Monegasque rookie who replaces Raikkonen at Ferrari next year, was an impressive seventh fastest.
At the back, McLaren's double world champion Fernando Alonso was slowest with team mate Stoffel Vandoorne 19th, and the Williams pairing of Canadian Lance Stroll and Russian Sergey Sirotkin just ahead of them.
(Reporting by Alan Baldwin, editing by Sudipto Ganguly)
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