Williams will next play 32nd seed Carla Suarez Navarro, who beat Germany's Andrea Petkovic 6-1 6-4.
The 27-year-old Londoner went down 6-0 6-3 to Germany's Andrea Petkovic at the tournament in Linz.
Action gets underway Sunday, but in the qualifying tournament Friday there was defeat for former World No.9 Andrea Petkovic.
Italian 14th seed Flavia Pennetta defeated Romania's Sorona Cirstea 6-1 1-6 6-1 to earn a second-round clash with German Andrea Petkovic.
Kuznetsova next faces Andrea Petkovic of Germany, who fought back from dropping the opening set to defeat another Russian, Elena Vesnina, 4-6 6-1 6-4.
Clijsters will next face German Andrea Petkovic, who secured her last-four spot with an upset 6-4 6-2 victory over fourth seed Daniela Hantuchova of Slovakia.
And there was a third shock when yet another Russian, French Open champion and fifth seed Svetlana Kuznetsova lost 7-5 4-6 6-3 to Germany's Andrea Petkovic.
Williams, who reached the Australian Open final in 2003, will play 30th seed Andrea Petkovic of Germany in the next round after she beat British number two Anne Keothavong.
Anna-Lena Groenefeld put Germany ahead in Brno with a 6-2 6-2 victory over Lucie Safarova, but Petra Kvitova leveled for the hosts with a 6-4 6-4 win against Andrea Petkovic.
The other Russian seeds in the women's tournament enjoyed better fortune as second seed Vera Zvonareva thrashed Germany's Andrea Petkovic 6-4 6-1, while number seven Elena Dementieva had to hold off the challenge of 40-year-old Kimiko Date Krumm 6-3 1-6 6-3.
Former world No. 1's and Serbian Fed Cup teammates Ana Ivanovic and Jelena Jankovic will attempt to recapture their best results while German trio Sabine Lisicki, Julia Goerges and Angelique Kerber are likely to make a push in the absence of world No. 10 Andrea Petkovic who withdrew Wednesday, citing a stress fracture in her lower back.
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