Brawn oversaw all seven of Michael Schumacher's world titles in addition to Jenson Button's in 2009.
But British hope Jenson Button starts from back in 17th after another disappointing qualifying session.
The 22-year-old Mexican who currently races for the Sauber team will partner Jenson Button from 2013.
Mark Webber, Fernando Alonso, and Jenson Button will start in second, third and fourth position.
British Formula One drivers David Coulthard, who retired this season, and Jenson Button are also racing.
Jenson Button sealed the drivers' championship with a fifth-placed finish while Rubens Barrichello was eighth.
Barrichello finished sixth behind Williams's Nico Rosberg and Jenson Button while Lewis Hamilton was last.
Barrichello was also third in the second session, just ahead of team-mate and championship leader Jenson Button.
The incident happened at the Tosa hairpin as the two battled for second place behind Jenson Button.
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Ferrari's Fernando Alonso starts in third ahead of the McLarens of Jenson Button and Lewis Hamilton .
Barrichello and new world champion Jenson Button dominated the early part of this year's title race with Brawn.
Hamilton will be alongside 10th-placed former McLaren teammate Jenson Button, who succeeded him as world champion in 2009.
Should he return, Schumacher would go head-to-head with fellow world champions Jenson Button, Lewis Hamilton and Fernando Alonso.
Australian Mark Webber was fourth fastest for Red Bull ahead of Barrichello's team-mate and championship leader Jenson Button.
Jenson Button had a puncture with three laps remaining and then had to retire on the penultimate lap.
McLaren's Jenson Button starts on the second row, ahead of Red Bull's Mark Webber with Ferrari's Fernando Alonso.
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Jenson Button will start at the back after he was forced to withdraw his Honda because of gearbox problems.
The Super Aguri driver joins Mark Webber, David Coulthard, Rubens Barrichello, Jenson Button and Alexander Wurz in being eliminated.
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Sandwiched between them in 13th is Britain's Jenson Button, who still believes there is more to come from Honda.
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Hamilton's team-mate Jenson Button briefly passed him on lap 48 only for Hamilton to repass at the next corner.
McLaren announced on Wednesday that they had signed Jenson Button for 2010.
The highlight of this second era running its own team was Jenson Button's win at the 2006 Hungarian Grand Prix.
His time of one minute, 26.801 seconds, was 0.25 seconds quicker than McLaren team-mate and current world champion Jenson Button.
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Juan Pablo Montoya was second fastest to book a spot on the front row while Jenson Button was third quickest.
As the 2008 world champion's fortunes improve, his former McLaren teammate Jenson Button continued his lackluster start to the 2013 season.
Hours after Jenson Button and Rubens Barrichello completed a dream one-two finish in Melbourne, chief executive Nick Fry announced the losses.
"It was way too wet out there and the decision to call it off was correct", said race winner Jenson Button.
Flushed by his first podium finish in F1, Jenson Button has insisted that his third place in Malaysia was no freak.
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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.
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