Williams, the tournament's No. 2 seed, withdrew early in the day with a left knee injury.
Govortsova, 19, of Belarus, squandered three match points on her serve in the ninth game of the second set, then capitalized on the fourth one with a forehand to the open court at 30-40 on Hantuchova's serve. Govortsova, who is ranked No. 43, admitted to some nerves after taking a 5-1 lead in the second set, especially since the 12th-ranked Hantochova had rallied in a similar situation to win their first meeting last year.
"When I was up 5-1 I started to think I'm going to win the match, then she started to play more aggressive,'' Govortsova said. "Then at 5-4 I started to hit the ball again and finally won. She hits the ball really deep and has a good serve. To beat her, you have to be aggressive.''
Hantuchova, who still is trying to find her form after a long layoff from a stress fracture in her right heel, said that her game is "not there yet. I just have to be patient, keep practicing and keep working hard. It's a long way back.''
Anna Chakvetadze, of Russia, the No. 3 seed, had no trouble in her second-round match, toppling Marta Domachowska of Poland, 6-1, 6-1, in 49 minutes.
Earlier in the day, before Stephanie Dubois of Canada closed out the first round by beating Playboy magazine cover girl Ashley Harkleroad, 6-2, 6-3, Wimbledon quarterfinalist Nadia Petrova moved into the second round of the East West Bank Classic on Tuesday with her first hardcourt win since January, a 6-0, 6-4 victory over Russian Alina Jidkova. She was joined in the second round by No. 10 Flavia Pennetta of Italy, No. 11 Nicole Vaidisova of the Czech Republic and No. 15 Dominika Cibulkova of Slovakia.
Williams had withdrawn Saturday at Stanford, but expressed a desire to play at the Home Depot Center over the advice of medical personnel and her father. But she said that after warming up Tuesday morning she knew she could not compete and joined sister Venus Williams, Lindsay Davenport and Svetlana Kuznetsova on the sidelines.
Top seed Jelena Jankovic, who could claim the No. 1 ranking in the world by winning here, will play her first match Wednesday against 98th-ranked American Vania King. Jankovic is coming back from a knee injury and has been idle since Wimbledon.
Pennetta was a 6-1, 6-0 winner over Stanford champion Aleksandra Wozniak; Vaidisova beat Ayumi Morita of Japan 6-7 (5), 6-3, 6-1, and Cibulkova ousted Monica Niculescu of Romania 6-4, 6-3. King set up her match with Jankovic by beating Angela Haynes 6-3, 6-3.
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