The 18-year-old will line up a career-high fifth on the grid for Sunday's race at Albert Park, having out-qualified former world champions and seasoned veterans in the first qualifying session of his second season.
World champion Lewis Hamilton led a Mercedes one-two for the front row, with Ferrari hogging the second row. Verstappen's team mate Carlos Sainz will line up seventh after also showing composure to reach the third and final session of the revamped format.
Sainz will start one ahead of Red Bull's Daniel Ricciardo with the Australian's team mate Daniil Kvyat starting 18th in the field of 22 after failing to advance to the second round of qualifying.
"We have to be realistic, Mercedes and Ferrari are a little too fast for us at the moment," Verstappen told reporters.
"But it was a great achievement by the whole team... I think you can call us 'best of the rest' at the moment.
"We knew the car was handling well but you don't know what other teams are doing.
"But I think we made a very good step, not only with the car but with the power unit. And everything worked perfectly today.
"I was quite on the limit, quite on the edge, but I think not many people made a mistake so I think we deserved to be P5," added Verstappen, who will bid to become the youngest points scorer in Australia.
"It should be positive in the race and we have a good chance to maintain position."
Former Toro Rosso driver Ricciardo said he was "happy" with his grid position but not relative to Red Bull's sister team.
"I would like to say (our pace) should be a little bit better than Toro Rosso," he said.
"It's just a case of whether we jump them at the start. Obviously they've got a bit more power this year with the engine they've got, so we'll have to work out a good strategy to get around it.”