Vettel, who retired with an engine failure, has slipped to fourth place 25 points adrift of Button with a maximum of 60 points available from the remaining six races.
Germany's Vettel is now 21 points behind Button with team-mate Webber just 1.5 points behind - and Webber the same margin ahead of Barrichello.
In the title race, Button has 15 points, five more than Barrichello.
"I went to the pool not to the track today, " said Vettel, who is 16 points behind Button in the championship.
Button's Brawn GP team-mate Rubens Barrichello finished behind the dominant Red Bulls in third place, to close to within 23 points of Button in the world drivers' standings, with Vettel breathing down the Brazilian's neck.
Webber, who battled with Button for more than half the race in Valencia, could finish only ninth as the Red Bulls struggled to find any pace on the stop-start street circuit and is now 20.5 points behind Button.
Brawn nonetheless backed Button to finish in the points, but said he hoped the title would be decided in Abu Dhabi.
He sits ninth in the 2009 drivers' championship, 42 points behind Brawn GP's English driver Jenson Button, while McLaren trail table-toppers Brawn by 73 points in the constructors' championship.
In the joke, a large arrow points to a red button and reads, emphatically, DO NOT PUSH THIS BUTTON.
If he won, Button needed Vettel not to score points to keep the championship alive but the German finished third behind Ferrari's Fernando Alonso.
Verhoeven points to the home button on the machine.
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Button, who leads Barrichello by 14 points in the drivers' championship, can still land the title in Sao Paulo.
"I need to have a good race here and challenge for the victory to claw some points back, " said Button.
Button, who leads the standings by 14 points, will start the Brazil Grand Prix in 14th, with Barrichello on pole.
And while Button leads the drivers' championship by 21 points following his fifth place in Germany, Barrichello was leapfrogged by Red Bull drivers Sebastian Vettel and Mark Webber and now sits fourth.
Vettel's second success of the season leaves him 25 points behind world championship leader Jenson Button -- who disappointed the home fans by finishing down in sixth place, the position he started from on the grid.
Button, fastest in first practice, is 35 points behind McLaren team-mate Lewis Hamilton, who tops the table.
After picking up just two points in the opening two races, Button will start Sunday's race from eighth.
On some you press a button for a candidate and a bright green arrow points to the candidate.
Hamilton leads the title race by three points from Webber, with Vettel, Button and Alonso needing to make up ground.
Brawn's Button remains in the world championship lead on 68 points but Vettel and Webber have leap-frogged over Barrichello, who angrily accused his own team of costing him victory after the race.
"Seb had a big top speed advantage, " said championship leader Webber, who is now on 93 points, five ahead of second-placed Button.
Red Bull will want to take points out of Brawn's championship leader Jenson Button and, of course, they want to win the race.
The result means that Button extends his lead over the Brazilian by one point to 15 points with three rounds of the championship to go.
Button was ranked 18th in the drivers' standings, contributing only three points.
Button cruised to a comfortable victory - extending his championship lead to 12 points, while Vettel fought off a challenge from Trulli in the closing laps.
Button's disappointing season continued when he failed to finish in the points after being sent out from his final pit stop with a loose front wheel, having been fifth at one stage.
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Alonso took his points total for the season to 194 after finishing third, while Button continued his impressive run of form with a second placed finish.
But he used his Kers power-boost button to good effect to keep the German behind and score Ferrari's first points of the year.
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