Hamilton, who has a 10-point advantage over German team mate Nico Rosberg after winning the last three races, produced the fastest lap yet of the new Sochi circuit with a best time of one minute 38.726 seconds.
The 2008 champion spun late in the session at the penultimate corner, but escaped without damage.
"It was a tremendous lap, he seems to extract the maximum out of the car at the moment," Mercedes motorsport head Toto Wolff said.
"Somehow, Lewis seem to nail it on first lap, Nico seems to struggle a bit more, but this is just practice," the German told the BBC.
Rosberg was second fastest, 0.290 slower, on a warm and bright morning at the 5.8km track that snakes around the Black Sea resort's imposing Olympic Park venues used for this year's Winter Games.
Hamilton, chasing his ninth win of the season on Sunday, was also fastest on Friday, although Rosberg was quicker in the morning.
Finland's Valtteri Bottas was third for Williams in a session that was briefly halted after the McLaren of Danish rookie Kevin Magnussen stopped on track with a gearbox problem that will bring a five-place grid penalty.
Red Bull's Australian Daniel Ricciardo, the only driver other than the Mercedes duo to win this season, was fourth fastest.
Venezuelan Pastor Maldonado failed to set a lap time with mechanics working on his Lotus.
Sunday's race comes after a dark weekend in Japan, with Marussia's Jules Bianchi critically injured in hospital after the Frenchman crashed into a recovery tractor. Britain's Max Chilton is the team's sole driver in Sochi.
(Editing by John O'Brien)
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