The absence of F1 minnows Caterham and Marussia meant just 18 cars took to the track for the first time since the 2005 Monaco GP, and points leader Hamilton was the only driver to lap in the 1m39s as he beat team-mate Rosberg to the top spot by just under three tenths of a second.
McLaren led the way for most of the session, despite technical problems enforcing radio silence between the pitwall and both drivers.
Jenson Button ran the Mercedes drivers close and ended the session less than a tenth slower than Rosberg.
Russian Grand Prix
Hamilton hails Mercedes after securing history-making 100th win in the wet
Team-mate Kevin Magnussen also enjoyed a spell at the top of the times early on, but he slipped to fifth in the final classification, a tenth behind Daniil Kvyat's Toro Rosso.
Ferrari trialled experimental front and rear wings in this session, as well as checking driver visibility should it decide to raise the height of the top surface of the nose on next year's car.
Fernando Alonso rounded out the top six, 1.124s off the pace, while Kimi Raikkonen was 12th quickest in the sister car.
Four-time world champion Sebastian Vettel, who is set to start from the pitlane on Sunday after breaching rules that limit the number of engines he is allowed to use across the season, set the seventh quickest time in his Red Bull-Renault.
Team-mate Daniel Ricciardo ran into engine problems of his own early on in the session, which restricted him to the 17th fastest time and meant he completed just five laps.
Romain Grosjean was the only driver to lap slower than Ricciardo, as he trialled an experimental non-twin-tusk nose on his Lotus E22.
Max Verstappen made his second free practice appearance of the season, taking over the Toro Rosso normally raced by Jean-Eric Vergne.
The Dutch teenager lapped nine tenths off Kvyat in rounding out the top 10, just behind Williams reserve Felipe Nasr - in Valtteri Bottas' car - and Force India's Nico Hulkenberg.
Cars returned to the circuit at the end of the session to allow the FIA to trial a new yellow flag speed limit set to be implemented to improve safety following Jules Bianchi's Japanese GP crash.
Russian Grand Prix
Hamilton overtakes Norris in Russia rain to take 100th win, Verstappen steals second
Russian Grand Prix
Russian Grand Prix As it happened - Hamilton takes dramatic win