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The Briton, whose previous best grid position was third in Belgium in his debut season with Williams, set a stunning lap of one min 19.753 sec to give Schumacher a tough target to beat.
And the German driver, who claimed pole and victory in all three of the season's preceding races, made a crucial mistake at the Variante Alta, and left Button to claim BAR's first ever pole position.
Schumacher will start alongside Button from second place after finishing 0.258 seconds behind with Colombian Juan Pablo Montoya, who was the last man out on track in his Williams, in third.
Brazilian Rubens Barrichello finished fourth fastest in the second Ferrari with German Ralf Schumacher, of Williams, fifth and Spanish Renault driver Fernando Alonso sixth.
Takuma Sato finished 1.160 seconds down on his BAR team-mate in seventh place with Australian Mark Webber eighth for Jaguar, Italian Jarno Trulli ninth for Renault and Brazilian Cristiano da Matta completing the top ten for Toyota.
Hungarian Zsolt Baumgartner was the first man out but he spun his Minardi at the Variante Alta, where he had crashed in the morning practice sessions, and aborted his lap so that he could change his engine before the race.
Flying lap
Finn Kimi Raikkonen, who has failed to finish a race this season, also chose not to complete his flying lap and change his engine and will start from the back for the second consecutive race.
Alonso was the first lead runner out on track after finishing a lowly 14th fastest in first qualifying and he set a competitive time of one min and 20.895 secs that his team-mate Trulli could not better.
Webber also failed to improve on Alonso's effort as he finished a close second after the first ten runners had completed their laps. Sato also failed to better Alonso but moved ahead of Webber on his run.
Barrichello, however, comfortably raised the bar when he moved 0.444 seconds ahead of Alonso but Italian Giancarlo Fisichella lost his chance to set a time when his Sauber team failed to repair his car before the deadline for his run.
Button then bettered Barrichello's lap by a stunning 0.698 seconds and David Coulthard compounded McLaren's misery by finishing 1.338 seconds off the pace with just Schumacher and the Williams pair left to run.
Montoya had set the fastest time in the earlier qualifying session that determines the running order for the crucial grid-deciding runs after finishing more than six-tenths of a second quicker than his team-mate Ralf Schumacher.
