While Charles Leclerc was unable to repeat his session-topping Q2 time, clearing the way for Max Verstappen to grab pole position, Russell led the Mercedes charge by running third fastest.
Verstappen clocked a 1m29.179s effort aboard his Red Bull, with Russell crossing the line 0.306s down. Team-mate Lewis Hamilton, meanwhile, will start from ninth on the grid.
Russell heralded the Silver Arrows for having made significant progress with its qualifying performance thanks to the simulator work completed following the pre-season test.
Giving credit to the mileage put in by the simulator drivers – with the Mercedes line-up led by Frederik Vesti, Mick Schumacher and Anthony Davidson – Russell said: “We've had some really great drivers back at base doing the work in the simulator.
“Lewis and I have been back on the simulator as well, fine-tuning the set-up, making some improvements.
“We've obviously made a big step forward in single-lap – in the qualifying pace. We hope we haven't compromised the race pace at all. I think it'll be a close fight between everybody… other than Max.”
Russell underlined that he and Hamilton were much more comfortable in the new W15 challenger compared to its predecessors. The W14 especially was known for its spikey rear axle.
However, despite the more compliant drive, Russell – who qualified sixth in Bahrain last year – acknowledged that Mercedes still had a long way to recover to take the fight to Verstappen.
“Everybody at the factory has done an amazing job to give Lewis and I a car that we feel much happier with, a base that we can build upon,” said Russell.
“But ultimately, Max is still out there in front. We've still got some catching up to do.
“But I think when we look at our qualifying performances over the last two years in Bahrain and our race pace, starting P3 is a great place…
“Red Bull is still so strong at the moment. Max is doing a really great job. He's got the new tyres as well.
“I think if there's an opportunity to take the lead, we'll go for it. But ultimately, I think the race for all of us is for second…let's hope for some craziness.”