Germany's Nico Rosberg finished sixth for Williams, with Spain's double world champion Fernando Alonso collecting two points for Renault and Frenchman Sebastien Bourdais eighth for Toro Rosso.
There was disappointment for Force India, chasing their first points finish, with Italian Giancarlo Fisichella finishing ninth.
McLaren's world champion Lewis Hamilton, who started last on the grid after crashing in qualifying, was 12th and lapped by his winning compatriot.
Button became only the seventh driver to win five of the first six races of a season, the last being Germany's seven-times world champion Michael Schumacher in 2004.
He was also the sixth British driver to win in the Mediterranean principality. Hamilton won last year's race.
In a race with few incidents, 14 cars finished. McLaren's Heikki Kovalainen, Red Bull's Sebastian Vettel, Renault's Nelson Piquet, Toro Rosso rookie Sebastien Buemi and Williams Kazuki Nakajima all crashed out.
Jenson Button (center) along with 2nd-placed teammate Rubens Barrichello (left) and 3rd-placed Kimi Raikkonen
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