Williams, who beat world No. 2 Victoria Azarenka in the second round, defeated 13th-seeded Simona Halep 4-6, 7-5, 6-3. It is only the third time this year she's made it as far as a tournament quarterfinal. She won her previous matches in the quarters but lost in both semifinals.
Williams battled Halep for 2 hours, 25 minutes, as she came back from a one-break deficit three times in the second set and another time in the third.
Her next opponent has also knocked off seeded players in the last two rounds. Eugenie Bouchard, who stopped ninth-seeded Sloane Stephens in the second round, eliminated No. 6-seeded Jelena Jankovic 7-5, 6-2 Wednesday. She won nine of the last 11 games to advance.
No. 2-seeded Agnieszka Radwanska beat 16th-seeded Dominika Cibulkova 6-3, 6-4 by winning 70 percent of the points on serve. Fourth-seeded Carolina Wozniacki took nearly 70 percent of the points in a 6-1, 6-1 rout of Magdalena Rybarikova and Angelique Kerber, the fifth seed, posted a 6-4, 6-2 win over 11th-seed Ana Ivanovic.
Lucie Safarova ousted 12th-seeded Samantha Stosur 6-4, 6-4 in the other match completed Wednesday. Two matches were suspended and will be finished Thursday.