Webber beat Nico Rosberg's time on his final lap, only for the 43-year-old Schumacher to surpass Webber's effort just moments later.
But the grid penalty Schumacher got at the Spanish Grand Prix means he starts from sixth on the grid on Sunday. The German has yet to earn a pole position since coming out of retirement last season.
Rosberg starts second and looks for his second victory of the season after winning the Chinese GP.
McLaren's Lewis Hamilton starts third, but teammate Jenson Button failed to make the final qualifying session for the second straight race.
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