Aston Martin's Fernando Alonso was fourth in a tight session that went to the wire.
Last year's winner Charles Leclerc claimed seventh in the Ferrari, with his teammate Carlos Sainz fifth.
It was a huge performance from Mercedes, who have struggled this season, with their speed clearly improving as they again bettered Ferrari.
Lance Stroll in the other Aston Martin will start sixth ahead of Leclerc with Williams' Alexander Albon a shock eighth.
Alpine's Pierre Gasly was ninth with Nico Hulkenberg in a Haas rounding out the top 10.
It is the second pole of the year for Verstappen, and the 22nd of his career, after the season-opening race in Bahrain, which he went on to win.
He started from 15th in Saudi Arabia a fortnight ago after mechanical problems, but sliced through the field to come second behind Perez.
The 25-year-old knocked out his rivals with a flying lap at the death of one minute 16.732, 0.236 secs ahead of Russell.
"I think the last run was very good, the whole weekend has been tough to get the tyres in the right window," said Verstappen, who has never won in Australia and will start on pole for the first time at Albert Park.
"Very happy to be on pole, already looking forward to tomorrow. I think we have a good race car but it is tricky on the tyres, so going to be an interesting race for sure."
But Mexico's Perez -- one point behind Verstappen in the championship standings -- had a horror of a day, struggling with grip and balance.
He left the track four times during the third practice and it didn't get any better in qualifying when he locked up and careened into the gravel at Turn 3 on his first lap.
He car beached and had to be removed by a crane, with the session red flagged.
"It was the same issue again," the dejected Perez said on the team radio.
Russell was ecstatic with Mercedes' performance, saying "we weren't expecting that, that's for sure".
"What a session for us. The car felt alive, and to be honest I'm disappointed I didn't get pole as the car felt awesome," he added.
Verstappen topped Q2 from Alonso and Sainz with Alpine's Pierre Gasly a casualty.
AlphaTauri pair Nyck De Vries and Yuki Tsunoda also missed out, along with Kevin Magnussen in his Haas and McLaren's Lando Norris.
Verstappen was also fastest in Q1 ahead of Russell and Hamilton.
Along with Perez, Alfa Romeo's Zhou Guanyu and Valtteri Bottas, Williams' Logan Sargeant and rookie McLaren driver Oscar Piastri all failed to get out of Q1.
