Mercedes got its Silverstone weekend off to a bad start on Friday when Russell and team-mate Lewis Hamilton were only 12th and 15th respectively in FP2.
However, after overnight work, helped by a sim session that Mick Schumacher reported on social media that finished at 2:15am, the W14 was in much better shape on Saturday.
Russell and Hamilton qualified sixth and seventh behind the Red Bull of Max Verstappen, the two McLarens, and the two Ferraris.
"Yesterday after FP2 strategy had us down as 17th and 18th quickest in single lap work, and third and fourth quickest on the race pace,” said Russell after the session.
"So the only thing different between those two were the tyres. We made some really good improvements overnight. Frustrated to see we're only half a tenth from P3, that would have been an amazing result.
"But I felt happy with my lap. Lewis has been pushing me really hard all weekend, and I sort of stayed calm. It all came together on that last lap. And there's no reason we can't fight for P2, P3."
He added: "It's exciting these sessions, I think it makes it exciting for the fans, makes it tense from the driver's seat. But you've got to have faith in your team, faith in yourself.
"Fortunately, we did the majority of things right. I wouldn't say it was plain sailing through the session, Q2 was a bit tense. But we probably ended up where we deserve to be."
Source: Autosport