Williams had little trouble in getting past Anna Tatishvili 6-2, 6-3 in 61 minutes. Williams, despite dropping serve three times, won 60 percent of the points when serving and 63 percent off Tatishvili's serve.
Halep had won 17 of her last 18 matches since the middle of June, picking up her first three WTA titles in the process. But the schedule's pace seemed to take its toll Thursday as she retired Thursday after falling behind Flavia Pennetta 4-6, 7-5, 2-0.
Qualifier Richel Hogenkamp ousted sixth-seeded Lesia Tsurenko 6-1, 2-6, 6-3 by converting five of her six break chances and Mathilde Johansson stopped Andrea Gamiz 7-5, 6-2 in the final second-round match.
Williams draws fifth-seeded Lourdes Dominguez Lino in Friday's quarterfinals with Hogenkamp playing No. 3-seeded Klara Zakopalova in the other match in that half of the draw.