Hill produced the only clear overtaking manoeuvre of the day when he slipped by Rubens Barrichello.
Button's team-mate Rubens Barrichello scraped through into the second session but could manage only 14th place.
BBC: Hamilton edged out Ferrari's Kimi Raikkonen by 0.102secs
Button's team-mate Rubens Barrichello endured an incident-packed race but was impressed with the Brawn's durability.
Jenson Button sealed the drivers' championship with a fifth-placed finish while Rubens Barrichello was eighth.
Brawn's Rubens Barrichello, fighting with Vettel for second in the championship, will start fourth.
Rubens Barrichello was the unluckiest driver out there as his Williams's reliability problems got worse.
BBC: Sebastian Vettel beats Lewis Hamilton to Abu Dhabi pole
The RA107 car, driven by Button and Rubens Barrichello, will aim to raise awareness of climate change.
BBC: SPORT | Motorsport | Formula One | Honda not quick enough - Button
As for Button, he is back in eighth on the grid with team-mate Rubens Barrichello in 13th.
That will be welcome news to drivers Button and Rubens Barrichello, who faced huge problems last year.
The Briton led from start to finish, despite two safety car periods, with Rubens Barrichello second in Melbourne.
After a 1-2 in Australia with Button and Rubens Barrichello they lead the constuctors' championship ahead of Toyota.
The Super Aguri driver joins Mark Webber, David Coulthard, Rubens Barrichello, Jenson Button and Alexander Wurz in being eliminated.
BBC: SPORT | Motorsport | Formula One | Turkish GP qualifying as it happened
The work, owned by the same French family for at least 200 years, was known as Confesseur de Rubens.
BBC: Portrait of a Carmelite Monk by Van Dyck, circa 1617 to 1620
In the afternoon, Williams's Rubens Barrichello was seventh ahead of Kubica, the second Williams of Nico Hulkenberg and Rosberg.
The identity of Maldonado's 2012 teammate is still unclear, with speculation surrounding the future of veteran Brazilian Rubens Barrichello.
Montoya left the circuit, fuming about the decision of the stewards to penalise him for causing a collision with Rubens Barrichello.
BBC: SPORT | Motorsport | Formula One | Schumacher one step away
Hours after Jenson Button and Rubens Barrichello completed a dream one-two finish in Melbourne, chief executive Nick Fry announced the losses.
Schumacher totalled an incredible 144 points, with his Ferrari team-mate Rubens Barrichello some way behind in second place with 77 points.
He drew convincingly as Andrea Mantegna and Nicolas Poussin, Giovanni Battista Piranesi and Peter Paul Rubens, Thomas Gainsborough and Jean-Baptiste-Camille Corot.
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Rubens Barrichello was third for Ferrari, with Juan Pablo Montoya fourth, and Britons Jenson Button and David Coulthard sixth and ninth.
But the rain eased off and the Williams duo of Rubens Barrichello and Nico Hulkenberg posted the first times after 16 minutes.
BBC: Lewis Hamilton fastest in Friday Australian GP practice
Briton Jenson Button led home Rubens Barrichello barely a day after Branson confirmed a "substantial sponsorship" deal with the Ross Brawn-owned team.
Police are treating the death as suicide, district attorney Marc Rubens said.
But Button's team-mate Rubens Barrichello insists his felllow Brazilian has not changed.
Sotheby's says experts noticed brushwork more characteristic of Rubens' pupil Van Dyck.
BBC: Portrait of a Carmelite Monk by Van Dyck, circa 1617 to 1620
Police said the brothers, Paulo and Rubens Vieira, headed the corruption scheme.
Brazilian veteran Rubens Barrichello took the Williams over from novice team-mate Pastor Maldonado, whose test ended early with a crash on Friday.
BBC: Nick Heidfeld heads Fernando Alonso at his Renault test
Rubens Ricupero, one of ten former environment ministers consulted by the president before the veto, praises her attempt to strike a balance.
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Rubens Barrichello was also out of luck in the second revamped Ferrari.
Rosberg fills one of the two slots in the team caused by the departures of world champion Jenson Button and Brazilian Rubens Barrichello.
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