'Came alive'
Mercedes' Russell said he had struggled to get the tyres working properly but that everything changed on the final lap.
“I did something totally different on that last lap and it all came alive, the lap was awesome,” he added.
“I had a big moment at turn one but it just all came together. I was really surprised when I crossed the line, I knew it was a good lap but to be between the McLarens — just buzzing.”
French rookie Isack Hadjar qualified seventh for Racing Bulls, a strong response to his nightmare debut in Melbourne, with Mercedes' Andrea Kimi Antonelli eighth and Yuki Tsunoda ninth for Racing Bulls.
Alex Albon completed the top 10 in a Williams.
Verstappen's teammate Liam Lawson, already struggling just two races into the job, had another woeful qualifying and will start last.
“I've got to get a handle on it,” said the New Zealander.
“It was a messy session and had we not dealt with traffic and stuff like that it might have been OK, but to be honest it's still not good enough.
“I just need to get on top of it. I think it's just time. Unfortunately I don't really have time.”
Red Bull boss Christian Horner, asked if there was an emerging problem with a driver brought in to replace underperforming Mexican Sergio Perez and score solid points, agreed it had been a tough day for Lawson.
“We'll have a good look at it and go through it and try to give him the best car for tomorrow,” he said.
Australian Jack Doohan, who collected two penalty points for a collision in the sprint, also went out at the first hurdle and will start 18th with Alpine teammate Pierre Gasly 16th.