The Mercedes driver lapped in a best time of one minute 36.406 seconds, well inside the 2015 pole position time of 1:37.113 set by team mate Nico Rosberg, after also ending Friday fastest on the timesheets.
Hamilton is chasing a Russian Grand Prix hat-trick, having won the two previous races held at the former Winter Olympic venue, and needs a third on Sunday to rein in Rosberg's advantage.
Rosberg, who was second fastest in the session and 0.068 slower than Hamilton, has won all three races this season in addition to last three of 2015, and leads the Briton by 36 points in the standings.
The Ferraris of Sebastian Vettel, who will have a five-place grid penalty due to an unscheduled gearbox change, and Kimi Raikkonen were third and fourth.
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They were followed by the Williams pair of Felipe Massa and Valtteri Bottas with Dutch teenager Max Verstappen seventh for Toro Rosso and Jenson Button eighth for McLaren.
Russia's only current F1 racer Daniil Kvyat was 13th fastest for Red Bull.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
