Hamilton was .199 seconds faster than Bottas in cool, overcast conditions, followed by the two Red Bulls of Max Verstappen and Daniel Ricciardo. Needing to beat Hamilton in Sochi to cut into the British driver's championship lead, Vettel was fifth, .543 off the pace.
"Not ideal," Vettel's said. "We struggled with the tires, with or without traffic ... We have some catching up to do." The German driver added that he had problems with the car when simulating both qualifying and race runs.
Hamilton said he'd studied the track intensely after finishing fourth last year and his work paid off. "Sochi has been one of the weaker circuits for me in the past, particularly last year. So I've done a lot of work to understand the balance and see where I can improve," he said. "It's been a good day for us, so let's hope that it continues tomorrow."
Red Bull won't likely trouble the leaders in Saturday's qualifying session because both of its cars have grid penalties for engine changes. Ricciardo said he enjoyed the session despite knowing that he will be at the back of the grid on Sunday.
"It almost sounds silly but I enjoyed driving around here," Ricciardo said. "Having the hyper-softs (tires) and having more grip around the circuit made it a pretty fun track to drive, so it was a good day."
Understanding how the tires degrade is a key part of the strategy in Sochi, where the generally smooth, low-wear surface often allows teams to squeeze more laps than usual from their tires. In the first session, Vettel was .05 seconds faster than Verstappen. Hamilton was .28 seconds further back in third, using harder tires than the two cars in front.
Hamilton leads Vettel by 40 points with six races remaining in the season as they both chase what would be a fifth career championship title to move level with Argentine driver Juan Manuel Fangio. F1 great Michael Schumacher has a record seven titles.
Mercedes has won all four previous races in Sochi. Vettel took pole position last year but was overtaken at the start by eventual winner Bottas for his first career win. Alongside the Red Bulls at the back of the grid will be the two Toro Rosso cars of Brendon Hartley and Pierre Gasly, plus McLaren driver Fernando Alonso. They have various penalties for changing too many engine parts and other power unit components.
Red Bull switched engines for Verstappen and Ricciardo to return to an older Renault design from the more experimental "C-Spec" because of concerns about its performance at high-altitude races later in the season.
McLaren and Williams struggled in Friday's practice, with Williams driver Lance Stroll last in both sessions. He spun out in the first practice but avoided the barriers.
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