Hingis, who won here in 1998, posted a 6-1, 6-2 triumph over Japan's Ai Sugiyama. The Swiss teenager advanced to face 10th seed Barbara Schett of Austria for a berth in the quarterfinals.
Schett posted a 6-2, 6-1 victory over Poland's Magdalena Grzybowska.
Davenport also had an easy day, notching a 6-4, 6-2 triumph over Natasha Zvereva of Belarus. Davenport will meet France's Julie Halard-Decugis in the fourth round. Halard-Decugis, the ninth seed, upended Ruxandra Dragomir, 6-3, 4-6, 6-3.
Williams dropped the first set to Italy's Rita Grande but rebounded for a 4-6, 6-1, 6-2 triumph. The American teenager will meet Belgium's Kim Clijsters next. Clijsters posted a 6-3, 7-6 (8-6) victory over Russia's Tatiana Panova.
While Williams survived, fourth seed Nathalie Tauziat of France and eighth seed Anna Kournikova of Russia were not as fortunate. Tauziat was eliminated by Karina Habsudova of Slovakia, 6-4, 6-4 while Kournikova was bounced by Nathalie Dechy of France in a wild match, 7-5, 5-7, 7-6 (7-5).
Habsudova will meet Chanda Rubin of the United States in the next round while Dechy earned a matchup with Elena Dementieva. Rubin got by No. 11 seed Sandrine Testud of France, 6-4, 2-6, 6-2 while Dementieva defeated Magui Serna of Spain, 4-6, 6-4,6-4.
Fifth seed Mary Pierce of France and Conchita Martinez of Spain advanced today, as did American Monica Seles. Seles got by Switzerland's Patty Schnyder 6-0, 6-3 and will face Belgium's Sabine Appelmans in the fourth round. Appelmans erased Cara Black of Zimbabwe, 6-3, 7-6 (7-5).
Pierce moved past American Corina Morariu, 6-2, 4-6, 6-2 and will face 16th seed Elena Likhovtseva of Russia, who eliminated Mirjana Lucic, 2-6, 6-4, 7-5. Martinez upended Austria's Jelena Dokic, 6-2, 7-6 (7-4) and will meet Belgium's Dominique Van Roost, who posted a 4-6, 6-3, 6-0 triumph over Switzerland's Emmanuelle Gagliardi.
Hingis, 17-2 this year, leads Davenport by only 373 points in the latest WTA Tour rankings and it could have been even less had Davenport won their championship match at last week's State Farm Women's Classic in Scottsdale, Arizona. However, that clash never took place as heavy rain Sunday and Monday in the area canceled the match.
The men's portion of this event begins Monday. First prize for the women's champion is $330,000.