The world number one takes on Johanna Larsson of Sweden for a place in the last 16, the third step on the path to an Open Era record 23rd grand slam title.
Williams’ second-round win over fellow American Vania King brought her level with Martina Navratilova’s record of 306 grand slam wins.
"I knew it was on the horizon,” Williams said of the record. “I knew at Wimbledon that I wanted to get there. Obviously I'm excited about that. I would like to take one more step, several more steps."
Williams' troublesome right shoulder has held up well so far but she admits it is a constant battle.
“Just tons of treatment, tons of rehab, tons of ice,” she said. “It's constant.”
Fourth seed Agnieszka Radwanska, who could yet overtake Williams as world number one this fortnight, plays Caroline Garcia of France while sixth seed Venus Williams meets Germany’s Laura Siegemund.
In men's third-round action, Wimbledon and Olympic champion Andy Murray continues his quest for a second U.S. Open crown when he plays Italy’s Paolo Lorenzi.
Third seed Stan Wawrinka takes on unseeded Briton Dan Evans while sixth seed Kei Nishikori of Japan faces Frenchman Nicolas Mahut.
(Editing by Andrew Both)
