This year's schedule began with simultaneous events in China, Australia and New Zealand, and will climax with the season-ending championships in Turkey in late October.
The French Open and Wimbledon champion, looking to join Ivan Lendl and Pete Sampras as the only men to win the season-ending championships five times, powered through the set to win in one hour and 59 minutes.
The defeat effectively ends Schnyder's hopes of playing in the season-ending WTA Championships in Madrid next month.
The 31-year-old also beat Azarenka in the U.S. Open final and at the season-ending WTA Championships in Istanbul.
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She went on to win the season-ending WTA Championships in Doha, sealing the No.1 ranking in the last event of the year.
Olympic champion Williams has won the last two grand slams, at Wimbledon and the U.S. Open, and beat Sharapova in the final of the season-ending WTA Championships in Turkey.
In the women's draw, Li Na beat defending champion Agnieszka Radwanska of Poland 6-4 6-2 to secure reach the semifinals and seal her place in the season-ending WTA Championships in Istanbul.
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Last year Williams fell at the first hurdle in Paris -- a tournament she won back in 2002 -- before going on to triumph at Wimbledon, the Olympics, the U.S. Open and the season-ending WTA Championships.
It was Sharapova's third successive win over Errani, having also got the better of the Italian at the season-ending WTA Tour Championships.
But his hopes of ending the century on a high were shattered when a thigh muscle injury saw him pull out of the Paris Open in November, so ending his chances of booking a place in the season-ending ATP World Championships.
Safina lost her No. 1 ranking for the second time after retiring hurt during her first match at the season-ending Sony Ericsson Championships in Qatar in October, and revealed then that she had been struggling with the problem for three months.
Beckham is ending his career after helping his two most recent teams win championships.
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