Williams, winner at Wimbledon in July and at the Olympics this month, defeated Urszula Radwanska 6-4, 6-3.
The winning streak for Williams began after she lost in the opening round of the French Open and she is seeking her fourth straight tournament title.
Her quarterfinal opponent will be Angelique Kerber, who defeated Andrea Hlavackova 6-4, 7-6 (7-5).
No. 1 seed Agnieszka Radwanska, older sister of Urszula, advanced with a 6-4, 4-6, 6-4 decision over Sloan Stephens.
The match between Li Na and Johanna Larsson, the winner of which will meet Agnieszka Radwanska in the quarterfinals, was postponed by rain.
Samantha Stosur and Venus Williams also set up a quarterfinal meeting. Stosur ran over Ekaterina Makarova 6-1, 6-3 and Venus Williams was a 6-3, 6-0 winner over Sara Errani.
Anastasia Pavlyuchenkova won the first set over Caroline Wozniacki before their match was suspended by the bad weather. The winner of that one will meet Petra Kvitova, who ousted Peng Shuai 6-2, 6-2.