Hamilton started second on the grid behind Vettel and hunted him down, searing by him on the 42nd lap.
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Chevrolet's Rob Huff took race one, while team-mate Alain Menu took race two, despite Priaulx starting from second on the grid.
The third title contender, Red Bull's Sebastian Vettel, did even worse and will start 16th, with his team-mate Mark Webber second on the grid.
Button, who started from second on the grid, made a rare mistake as he drove into the side of HRT's Narain Karthikeyan and lost his front wing.
World champion Valentino Rossi remained upright throughout, and pinched second place on the grid with his last lap.
Alonso heads into Renault's home Grand Prix on the second row of the grid along with Toyota's Jarno Trulli.
Then they divided the whole brain into small sections with a three-dimensional grid and recorded the activity in each section of the grid for each second.
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The first of these activities was the ASEAN Emergency Preparedness Workshop, held in Bangkok in May 2012, and the second was the ASEAN Smart Grid Workshop, held in Hanoi in early November 2012.
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It is a hybrid because it uses software algorithms to combine two separate requirements: one is to ensure that the grid is capable of operating continuously, while the second is the ability to deal discretely with any system changes on the grid.
Button led a Brawn GP one-two, with teammate Rubens Barrichello finishing second after starting third on the grid and running strongly at the start.
Vettel's relegation will see Pastor Maldonado of Venezuela in his Williams promoted to third on the grid to share the second row with Kimi Raikkonen in his Lotus.
World champion Hamilton, 24, struggled with understeer on a crucial sector of a flying lap in the first session of qualifying, from which five drivers are knocked out, and ended up among the last five drivers on the grid for only the second time in his career.
The pair occupied the top two places on the grid before finishing first and second in their debut race in Australia and rivals fear a repeat this weekend.
ABB, a Swiss-Swedish engineering giant, has also developed brainy software that tracks grid flows several times a second and feeds the information to control systems that can respond within a minute or so.
Drivers can often be heard talking about their teams needed to improve their cars, about finding the elusive few tenths of a second per lap that will move them up the grid.
Vettel, whose grid-topping time was more than half a second faster than Webber, was delighted with his 10th pole of the season.
Lorenzo had fought from 20th on the grid to challenge Bautista and ALex De Angelis who took second.
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Sensors installed throughout the network send data about local grid conditions to a central computer, 30 times a second.
To keep power flowing reliably, grid operators must smooth out supply and demand on a second-to-second basis (known as frequency regulation), an hourly basis (intermittency), and on a daily, weekly, and annual basis (meeting peak demand).
Six more cars will then be eliminated during a second spell before the remaining top 10 cars battle it out for the grid positions.
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It was the German's first pole in five races and only the second time he has started a Grand Prix in first place on the grid in his home country.
Massa was later handed a three-place grid penalty after being accused of impeding Mark Webber in the second Red Bull during Q2, with the Australian qualifying eighth behind Lotus' Romain Grosjean.
Sebastian Vettel will start third on the grid after young Lotus driver Romain Grosjean, 26, snatched second place from the reigning world champion in the final seconds of the day's racing.
Heikki Kovalainen in the second McLaren overhauled Kimi Raikkonen's Ferrari to take third place on the grid.
After making up an easy place off the grid, the temptation of going inside the two Ferraris into the second chicane was easy to understand.
Mark Webber in the second Red Bull edged out seven-time world champion Schumacher with Button eighth on the grid.
But ubiquitous silicon and broadband have suddenly made such second-by-second tinkering with demand possible, and the idea of upgrading the century-old electric grid to make it more efficient isn't so crazy anymore.
"Practice starts during the weekend had shown that the dirty side of the grid was so lacking in grip that a car would lose up to a second in the 350-meter run to Turn 1, equivalent to two positions, " James Allen, a Formula One commentator for the BBC and the editor of jamesallenonF1.com, wrote in an email.
Honda's demise would also reduce the F1 grid to just 18 cars (nine teams) and would see them become the second team to fold this year following Super Aguri's closure early in the season.
Whitmarsh's approach is in stark contrast to that of other teams on the grid, with both Red Bull and Mercedes having issued driver orders during the season's second race in Malaysia.
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