Hamilton, 40 points clear of Ferrari's Sebastian Vettel with six races remaining, lapped Sochi's 5.8km Olympic Park circuit with a best time of 1m33.385s on the hypersoft tyres. Vettel ended up only fifth-fastest, in 1m33.928s, and behind the two Red Bulls driven by Max Verstappen and Daniel Ricciardo. His team-mate Kimi Raikkonen was sixth.
Vettel had been fastest in the morning with a best time of 1m34.488s, also on hypersoft tyres, with Hamilton third on the slower softs. He is running out of time to rein in Hamilton, who has seven wins to his name this season, including four of the past five. Mercedes has won every Russian Grand Prix since the first in 2014, with Hamilton twice victorious and team-mate Valtteri Bottas winning last year after now-retired Nico Rosberg in 2016.
Verstappen turns 21 on Sunday but cannot become the first 20-year-old to start on pole position due to a raft of engine penalties. He's one of five listed with confirmed drops to the back of the grid, leaving the exact starting order uncertain. His team-mate Daniel Ricciardo, Toro Rosso's Pierre Gasly and Brendon Hartley as well as McLaren's Fernando Alonso were the others hit with grid penalties.
Vettel took pole in Sochi in 2017 but Bottas made a lightning start to set up the win. The Finn was 0.199s slower than Hamilton in Friday's dry afternoon session. Ricciardo, fourth after lunch, had sat out much of the morning with mechanics working on his car.
Italian reserve Antonio Giovinazzi, who will step up to the Sauber race seat next season, took Marcus Ericsson's car for the opening practice while British teenager Lando Norris gained experience ahead of his McLaren debut in 2019. Giovinazzi was 10th fastest, with 18-year-old Norris - who went farming once but avoided the barriers - 13th.
McLaren regular Stoffel Vandoorne, who is ceding his place to Norris at the end of the year, was only 16th. Renault gave Russian F2 driver Artem Markelov a run in Carlos Sainz's car while Canadian Nicholas Latifi drove Sergio Perez's Force India.
1 Sebastian Vettel - Ferrari - 1m34.388s (HyperSoft)
2 Max Verstappen - Red Bull - 1:34.538 (HyperSoft)
3 Lewis Hamilton - Mercedes - 1:34.818 (Soft)
4 Valtteri Bottas - Mercedes - 1:34.999 (Soft)
5 Daniel Ricciardo - Red Bull - 1:35.524 (HyperSoft)
6 Esteban Ocon - Force India - 1:35.663 (HyperSoft)
7 Kimi Raikkonen - Ferrari - 1:35.696 (UltraSoft)
8 Kevin Magnussen - Haas - 1:36.196 (HyperSoft)
9 Nico Hulkenberg - Renault - 1:36.274 (HyperSoft)
10 Antonio Giovinazzi - Sauber - 1:36.712 (HyperSoft)
11 Romain Grosjean - Haas - 1:36.816 (HyperSoft)
12 Pierre Gasly - Toro Rosso - 1:36.944 (UltraSoft)
13 Lando Norris - McLaren - 1:37.022 (HyperSoft)
14 Charles Leclerc - Sauber - 1:37.054 (HyperSoft)
15 Artem Markelov - Renault - 1:37.183 (HyperSoft)
16 Stoffel Vandoorne - McLaren - 1:37.187 (HyperSoft)
17 Nicholas Latifi - Force India - 1:37.206 (HyperSoft)
18 Sergey Sirotkin - Williams - 1:37.225 (HyperSoft)
19 Brendon Hartley - Toro Rosso - 1:37.944 (UltraSoft)
20 Lance Stroll - Williams - 1:39.137 (HyperSoft)
1 Lewis Hamilton (Mercedes) 1m33.385s
2 Valtteri Bottas (Mercedes) 1:33.584
3 Max Verstappen (Red Bull) 1:33.827
4 Daniel Ricciardo (Red Bull) 1:33.844
5 Sebastian Vettel (Ferrari) 1:33.928
6 Kimi Raikkonen (Ferrari) 1:34.388
7 Sergio Perez (Force India) 1:35.122
8 Pierre Gasly (Toro Rosso) 1:35.137
9 Esteban Ocon (Force India) 1:35.147
10 Marcus Ericsson (Sauber) 1:35.295
11 Kevin Magnussen (Haas) 1:35.331
12 Carlos Sainz (Renault) 1:35.341
13 Charles Leclerc (Sauber) 1:35.432
14 Nico Hulkenberg (Renault) 1:35.568
15 Romain Grosjean (Haas) 1:35.911
16 Brendon Hartley (Toro Rosso) 1:36.024
17 Fernando Alonso (McLaren) 1:36.074
18 Stoffel Vandoorne (McLaren) 1:36.617
19 Sergey Sirotkin (Williams) 1:36.861
20 Lance Stroll (Williams) 1:37.001