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|Seven-time Grand Slam winner Venus Williams, pictured in July 2018, is the highest seed left in the WTA hardcourt tournament in San Jose, California AFP/Ben STANSALL|
Third-seeded Williams is the highest seed left in a tournament that saw second-seed Madison Keys follow top-seeded Garbine Muguruza in pulling out because of injury on Thursday.
Keys, the defending champion, pulled out with a right wrist injury before taking the court for her second-round opener against Australia's Ajla Tomljanovic.
"I have been feeling pain in my wrist over the last couple of days and felt worse today," said Keys, who was replaced in the draw by lucky loser Magdalena Frech.
Tomljanovic beat Poland's Frech 6-4, 3-6, 6-3 to book a quarter-final clash with fifth-seeded Romanian Mihaela Buzarnescu, a 7-5, 2-6, 6-1 winner over American teenager Amanda Anisimova.
Williams will take on Greece's Maria Sakkari, who dominated eighth-seeded Hungarian Timea Babos 6-0, 6-1.
Williams, who won the title in this event in 2000 and 2002, came back with a vengeance after dropping the second set to Watson. She broke the Briton three times in the final set, dropping just four points on her serve.
"It was a tough match and she played incredible. There were times where I had no answers," said Williams, who said her goal was to "control the points and enjoy the battle, just get out there and try to do what I know that I can.
"It worked out, thankfully."
Williams, now the highest-ranked player in the draw, will kick off Thursday's night session against Great Britain's Heather Watson.
Buzarnescu said she felt the pressure against qualifier Anisimova.
"She's from the new generation, and I'm from the old one, and I knew the pressure would be on me because she has nothing to lose," the Romanian said.
The other two quarter-final match-ups were decided on Wednesday, when Britain's Johanna Konta followed up her stunning defeat of Serena Williams with a straight-sets victory over US teenager Sofia Kenin to book a meeting with fourth-seeded Elise Mertens of Belgium.
American Daniell Collins will take on former world number one Victoria Azarenka for a place in the semi-finals.