Williams, coming off a tournament victory 2½ weeks ago in the Swedish Open, set up a match Friday against Slovakia's Magdalena Rybarikova.
"She wasn't able to play her game as much as she wanted to," Williams said. "When you play such a high-ranked player, you have to go in there with the mindset of do the best you can before they can step all over you and do well."
Wimbledon champion Marion Bartoli retired because of an abdominal injury early in the second set of her match against Rybarikova.
"Kind of excess of tiredness and exhaustion on my body they feel," Bartoli said. "But it's so large, the pain is so large and we can't really say right now exactly (if) there is a tear at some point or if it's just like a huge tightness."
Rybarikova led 7-6 (5), 1-0 when the seventh-seeded Bartoli stopped playing.
Playing her first event since returning from a hamstring injury that sidelined her since her major victory in London, Bartoli was in obvious discomfort as she walked to the player bench area, where she had a trainer stretch her arm and leg.
"Everything that happened for me since a month (ago), it's not without any tiredness," Bartoli said. "And obviously it took me so much energy to win my first Grand Slam that at some point I will have a kind of low and it's normal. I'm human. At the end of the day I can't be winning after winning after winning without feeling at some point a kind of exhaustion."
Third-seeded Agnieszka Radwanska of Poland also advanced to the quarterfinals, beating American Sloane Stephens 6-1, 7-6 (2). Fifth-seeded Sara Errani of Italy beat Alize Cornet of France 7-5, 7-6 (3); and Romania's Sorana Cirstea edged Serbia's Jelena Jankovic 6-3, 6-4.
In late matches, sixth-seeded Petra Kvitova of the Czech Republic beat 12th-seeded Samantha Stosur of Australia 6-3, 6-3; and Slovakia's Dominika Cibulkova topped 10th-seeded Roberta Vinci of Italy 6-3, 7-6 (4).