Kubica's team-mate Nick Heidfeld and the second Toyota of Jarno Trulli completed the top 10.
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The Englishman was demoted to third place behind Ferrari's Felipe Massa and BMW Sauber's Nick Heidfeld.
Russian Vitaly Petrov initially partnered Nick Heidfeld before Brazilian Bruno Senna replaced the German in August.
And he was third fastest overall on Saturday, behind Nick Heidfeld in the Renault and Fernando Alonso's Ferrari.
The team have replaced Pedro de la Rosa with Nick Heidfeld for the final five races of this season.
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Nick Heidfeld was a fine fourth for Williams with team-mate Mark Webber sixth.
German Nick Heidfeld and Britain's Anthony Davidson, who impressed as BAR's test driver last season, are also in the running.
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Germans Nick Heidfeld of BMW Sauber and Nico Rosberg of Williams were seventh and eighth in the final points positions.
Nick Heidfeld completed a BMW one-two with Red Bull's David Coulthard third.
But Renault's sixth-placed Alonso followed by Sebastian Vettel and BMW Sauber's Nick Heidfeld will all be expected to push hard from the start.
However, BMW Sauber's Nick Heidfeld was left bemused by Mosley's comments.
Williams' Nico Rosberg claimed fifth spot with Ferrari number two Felipe Massa sixth, the other McLaren of Heikki Kovalainen seventh and BMW Sauber's Nick Heidfeld eighth.
Nick Heidfeld was seventh for a resurgent BMW Sauber, with Ferrari's Kimi Raikkonen eighth, followed by the Williams of Kazuki Nakajima and Toro Rosso's Sebastien Buemi.
Countryman Rosberg, 24, has already been signed up, but the team's second driver has yet to be confirmed, although they have also been linked with Nick Heidfeld.
Germany's Nick Heidfeld, still seeking to clinch a new contract with BMW Sauber, was the biggest casualty of the first qualifying session as he could finish only 16th.
The BMW Sauber team, who currently have Robert Kubica and Nick Heidfeld as their drivers, held a meeting on Tuesday where they made the decision to quit the sport.
Nick Heidfeld, who set the fastest lap in final practice, kept up his improved run of form to take fifth for BMW Sauber with team-mate Robert Kubica in eighth.
Despite the problem, Raikkonen ended the day fastest in testing ahead of Jarno Trulli of Toyota by about one tenth of a second, with BMW Sauber's Nick Heidfeld further behind.
Justin Wilson was 19th for Minardi, saved from starting last by Sauber's Nick Heidfeld who hit technical problems at the first corner and stalled in front of thousands of his countrymen.
Brawn have now been renamed Mercedes Grand Prix and have already signed German Nico Rosberg as one of their drivers, with his compatriot Nick Heidfeld the favourite for the second seat.
Kubica and BMW Sauber team-mate Nick Heidfeld, who finished among the final five slowest times in both sessions, struggled with brake balance with Kubica even describing it as a "disaster" early on.
Nick Heidfeld of BMW took fifth after McLaren's Heikki Kovalainen suffered a puncture with 20 laps to go, with Toyota's Timo Glock and Renault's Nelson Piquet taking the final points positions in seventh and eighth.
Hamilton took the checkered flag ahead of Massa and Nick Heidfeld, only to be demoted to third when stewards punished his corner-cutting during his battle with Raikkonen by adding 25 seconds to his time.
The McLaren pair were cruising back to the pits slowly to save fuel at the end of qualifying in Malaysia when they were narrowly avoided by BMW Sauber's Nick Heidfeld and Renault's Fernando Alonso on their final qualifying laps.
Podium finishes will be the main aim in 2008, after finishing fourth eight times in 2007, and winning a grand prix remains a possibility for drivers Nick Heidfeld or Robert Kubica, who team up for a second consecutive season.
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