The British driver made history for Brawn GP by winning the team's debut race in Australia in March and has won three of the last four F1 races this season.
With a sound strategy concocted by team principal Ross Brawn, Button and Brawn GP further pad their leads in both the drivers' and constructors' championship.
Button now leads the drivers' championship with 31 points, 12 points ahead of his teammate Rubens Barrichello, who finished fifth in Bahrain.
For the Constructors Championship, Brawn GP is on top with 50 points - nearly double Red Bull's 27.5 points and Toyota's 26.5 points.
After winning the Chinese Grand Prix last week, Red Bull's Sebastian Vettel settled for second place.
Toyota's Jarno Trulli stood on pole position at the start of the race but his light fuel load and his slow start at the line jeopardized his track performance. He still managed to land on the podium with a third-place finish.
Falling short of a podium finish was Lewis Hamilton, last year's winner at the Bahrain International Circuit. Even with the aid of his KERS (kinetic energy recovery system), Hamilton just couldn't fight for the lead but he still earned some points for landing on fourth at the chequered flag.
Kimi Raikkonen, meanwhile, scored Ferrari's first points of the season with a sixth-place finish while the ill-timed use of a harder compound tire ruined the performance of Toyota's Timo Glock, landing him on seventh place. Renault's Fernando Alonso claimed the final points-paying position at eighth place.
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