Russell qualified 14th in Sochi, one position ahead of Ferrari driver Vettel who exited Q2 after spinning and making heavy contact with unforgiving walls.
Confessing himself as "pleased" with the result, Russell said the team had feared it could have been consigned to the back row after poor showings in the practice sessions.
"It was a really good lap," the Williams driver told Sky Sports F1.
"Just getting Sebastian at the end as well which was a bonus. I’m really pleased.
"We thought we were a bit behind the Alfas and the Haas on pace before the session. So that was our main goal, to try and out-qualify them."
Both Haas and Alfa Romeo cars were eliminated in Q1 alongside Russell's Williams team-mate Nicholas Latifi who qualified 19th.
The session marked the sixth occasion that Russell has escaped the first phase of qualifying in 2020, and the Briton says Williams is now focussed on turning its strong Saturday pace into Sunday results.
He added: "The last couple of weekends we have been focusing more on the Sunday as we have recognised our Saturday pace has been good, but our Sunday pace has not quite matched it.
"We have rebalanced our quali and race pace here, which will put us in a good position tomorrow.
"I think Haas and Alfa still have the edge on us, so I think it will be a race to drive as quick as I can and check my mirrors to make sure they are not going to overtake me."
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.