The American, 34, won 6-2 6-3 to pass Roger Federer in the all-time list of matches won at the tennis majors.
She moves on to the quarter-finals, where she will face Romanian fifth seed Simona Halep, who beat Spain’s Carla Suarez Navarro 6-2 7-5.
“It’s a huge number,” Williams said of her record 308th win.
“I think it’s very significant actually. I definitely never thought I would be playing still. Now I don’t really see when I’m going to stop.
“I’m just enjoying these moments out here, getting to break records that I didn’t even know existed or I didn’t even know was possible.”
Halep has lost seven of eight matches against Williams but hopes that will at least keep the pressure off in their quarter-final.
Croatian teenager stuns Radwanska
Ana Konjuh, 18, became the first Croat to reach the women’s quarter-finals at the US Open with a shock 6-4 6-4 win over fourth seed Agnieszka Radwanska.
Konjuh hit 38 winners including six aces as she avenged a second-round loss to her Polish opponent at Wimbledon.
“It’s been an incredible night,” said the 2013 US Open junior champion after she made it past the third round of a Grand Slam for the first time.
“This time I got revenge, so I’m really happy.”
Konjuh will now face Czech 10th seed Karolina Pliskova, who saved a match point as she beat Venus Williams 4-6 6-4 7-6 (7-3).
“Whenever you have a match point on someone else’s serve, it’s a little bit of an asterisk,” said Williams. “I really have no regrets on that.”