Williams saved two set points in the tiebreak despite a sore right ankle and made the decisive break for a 6-5 lead in the second before serving out the match at love.
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"I really wanted it for myself," Williams said. "I just let go and relaxed."
The tournament features the top eight players in the world. The top two from each group advance to the semifinals. Top-ranked Dinara Safina and No. 4 Caroline Wozniacki play their first matches on Wednesday.
Kuznetsova, the French Open champion, led 6-4 in the first tiebreak but Serena erased the first set point with a return winner and the second with an ace -- after a challenge to overturn the line judge's call that the serve was out.
Serena had led 3-1 earlier in the tiebreak and said she let her focus slip before closing it out.
"I thought I had ruined it. I missed a chance to go up 4-1," she said. "I started thinking about how I was going to play in the second set. The next thing I knew, I was still in the tiebreaker."
After trading breaks early in the second, Kuznetsova had a game point on serve at 5-5 but double-faulted twice to give Serena a break opportunity, which the Wimbledon and Australian Open champ converted with a return winner.
Serena played with tape on both ankles and needed to have the right one treated and re-taped after the first set.
"I rolled it in the tiebreaker, and I was like 'Oh no!'" Williams said. "But it turned out well."
She will play Venus on Wednesday and can secure a spot in the semifinals with a win. In the other matches, Wozniacki plays Azarenka and Safina takes on Jankovic.
Aside from a winner's check of up to $1.55 million, Safina and Serena, ranked second, are also vying for the year-end No. 1 ranking. Safina's margin is so slim that the player who performs best here will end 2009 atop the list.
Venus had a chance to serve out the match at 6-5 in the second set but Dementieva's backhand passing shot forced the tiebreak. Then the American's game fell apart in the deciding set as Dementieva raced out to a 4-0 lead. The Russian, who struggled with her serve in the first two sets and finished with 15 double-faults, converted her second match point with a running backhand winner at the net.
"She hung around and stayed in there," Venus said. "She kept the ball in the court and did really well. I didn't put the ball in the court, and that didn't help."
Jankovic looked sluggish and error-prone from the start and was broken in the first game. She finished with 33 unforced errors, to 15 by Azarenka.
"I basically gave her everything. I beat myself," Jankovic said. "I just was trying to get in the match, get my rhythm. But unfortunately, that never happened. ... I was really a shadow of myself."
Azarenka is making her first appearance in the $4.55 million tournament, while Jankovic qualified for the third time.
"I'm glad she gave me the match, and she was not in the mood," Azarenka said. "It worked out pretty well for me."
Copyright 2009 by The Associated Press
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