Mara Santangelo celebrates her victory over Nadia Petrova

Russian Petrova, who struggled past a Polish junior player in her opening round, lost 6-3 6-3 to world number 31 Mara Santangelo of Italy.

Petrova hurled her racquet to the ground in frustration as she dropped 10 out of 11 points in the first set.

Unseeded Williams beat Dutch player Michaella Krajicek 6-4 6-3.

After Tuesday's snowy cold snap, conditions were much better in Warsaw, which pleased the American.

"I was just glad it was a lot warmer," she said. "On Tuesday, I was prepared to play in the snow, so this was definitely an upgrade.

"I feel like I have an opportunity and it's wonderful to be doing what I love."

Williams, who is unseeded after an injury-plagued 2006, now faces another player on the comeback trail, seventh seed Elena Dementieva.

Third seed Svetlana Kuznetsova dropped the opening set before beating Ukrainian qualifier Kateryna Bondarenko 2-6 6-2 6-1.

Sixth seed Anna Chakvetadze also reached the next round, beating Italian Tathiana Garbin 6-2 6-2.