By Nick Mulvenney
French driver Romain Grosjean sprung the biggest surprise by steering his Lotus to the third fastest lap and he will line up alongside the Mercedes of seven-times world champion Michael Schumacher on the second row.
Vettel, who claimed a record 15 pole positions last season including on his way to victory at Albert Park, was sixth fastest just behind his Red Bull team mate and Australia's great hope Mark Webber in fifth.
It was a major setback for a team that took 18 poles in 19 races last year and Sunday will mark the first time they will not have a driver on the front row since the 2010 Italian Grand Prix at Monza.
"It's an incredible feeling to be back here and to get off to such a good start," said Hamilton, who won at Albert Park from pole position in 2008.
"I think it's my and Jenson's first one-two in qualifying so it's fantastic to start the season this way. It's going to be incredibly tight and tense in the race."
Button was equally delighted to lock up the front row for McLaren for the first time since Hamilton and Heikki Kovalainen at the 2009 European Grand Prix.
"It is only the beginning but this is great first result for us on a Saturday and it looks like it's going to be a very exciting season," Button, who won in Melbourne in 2009 and 2010, said.
Mercedes driver Nico Rosberg and Pastor Maldonado of Williams will be on the fourth row of the grid after finishing seventh and eighth quickest.
Ferrari's problems continued with both cars failing to reach the final round of qualifying.
Former world champion Fernando Alonso spun off into the gravel in the second session while running fifth fastest and will line up 12th on the grid, while Brazialian Felipe Massa's miserable run of form continued with the 16th fastest time.
Another former world champion, Kimi Raikkonen, failed to get through the first phase of qualifying on his return to Formula One after two years away.
The 32-year-old Finn lost control of his Lotus on a corner on his final flying lap and will line up in 18th place on the ninth row of the grid for Sunday's race, barring any penalties for other drivers.
The former Sauber, McLaren and Ferrari driver also suffered the embarrassment of being resoundingly outqualified by the inexperienced Grosjean, who has never raced at Albert Park and will be starting his eighth race on Sunday.
The two HRT cars both failed to get inside 107 percent of the best time in the first session and therefore failed to qualify for the race for the second successive year.
(Editing by Alastair Himmer)