The 29-year-old Briton, successful in Australia and Malaysia and third in last weekend´s rain-soaked race in China, came home 7.2 seconds ahead of German Sebastian Vettel of Red Bull, the victor in China.
The win moved Button up to 31 points in the drivers´ championship.
Italian Jarno Trulli, who started from pole for Toyota, finished third ahead of defending world champion Lewis Hamilton in his McLaren Mercedes and Brazilian Rubens Barrichello of Brawn.
Next came Kimi Raikkonen, who finally claimed points for Ferrari, so ending their hugely-disappointing start to this season and avoiding the ignominy of recording their worst start in history.
Button´s win was conjured up by team chief Ross Brawn who produced a commanding strategy from the pit wall.
It was a supremely-crafted victory by Button who started from fourth on the grid and delivered a masterly drive that proved he had the capacity to wring out a victory when it was not, as he predicted ´a walk in the park´.
It was another glorious day for the Brawn team, watched closely by Sir Richard Branson, head of the Virgin Group who are poised to become their major long-term sponsors.
Created out of the ruins of the defunct Honda outfit, Brawn are on top of the constructors title race with a clear advantage of 22.5 points ahead of Red Bull.
German Timo Glock finished seventh for Toyota, ahead of two times champion Spaniard Fernando Alonso of Renault, in eighth place.
Button leads Barrichello by 12 points in the drivers´ standings, with Vettel one point further back in third.
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