Updated

Two-time champion Serena Williams was an easy round-robin winner, as the 2012 WTA Championships commenced Tuesday in Istanbul.

The third-seeded former world No. 1 great took care of fifth-seeded German left-hander Angelique Kerber, 6-4, 6-1.

The 2012 Wimbledon, U.S. Open and Olympic champion Williams is a two-time WTA Championships titlist and two-time runner-up, with her last title in the event coming three years ago.

Play actually got underway on Day 1 when Poland's Agnieszka Radwanska beat reigning champion Petra Kvitova of the Czech Republic indoors at Sinan Erdem Arena. The fourth-seeded 2012 Wimbledon runner-up to Williams Radwanska whipped the sixth-seeded 2011 Wimbledon champion Kvitova, 6-3, 6-2.

Kvitova defeated current world No. 1 Victoria Azarenka in last year's final in Istanbul, which will also play host to this elite eight-player event next year.

Also on Tuesday's schedule, second-seeded former No. 1 Maria Sharapova will meet seventh-seeded Sara Errani in a rematch of the 2012 French Open final, which was won by the big Russian in June.

This week's four-player Group A features the current No. 1 and Australian Open champion Azarenka, Williams (1-0), Kerber (0-1) and eighth-seeded Li Na, while Group B boasts the 2004 champion and 2007 WTA Championships runner-up Sharapova, Radwanska (1-0), Kvitova (0-1) and Errani.

The top-two players in each group will advance to the semifinals, and the winners will square off in the lucrative finale on Sunday.

Azarenka needs only two wins this week to end the year at No. 1.

The winner of this $4.9 million season-ending event could collect as much as $1.75 million.