The eight-player tournament divides the players into two groups and those within each group play a round-robin schedule to determine Saturday's semifinalists.
The Williams sisters are in the same group along with Svetlana Kuznetsova and Elena Dementieva. Serena defeated Kuznetsova, the French Open champion, 7-6 (8-6), 7-5.
Dementieva won for the first time in seven tries against Venus 3-6, 7-6 (8-6), 6-2.
In the other group, Victoria Azarenka was a 6-2, 6-3 winner over former world No. 1 Jelena Jankovic. Dinara Safina and Caroline Wozniacki will not play until Wednesday.
Results from this week's tournament will determine whether Serena Williams or Safina will finish the year as the world's top-ranked player.
Safina and Williams have traded the No. 1 ranking over the last two months and Safina currently has a narrow lead at the top.
To finish a season ranked No. 1 for the second time in her career, Serena must win one more match than Safina this week. If Safina wins more, or if they win the same number of matches, Safina will be No. 1 at the end of a year for the first time.
The Williams sisters will meet on Wednesday. If a player goes unbeaten this week, she will win $1.55 million.
Copyright 2009 by United Press International.
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