Top-seeded Serena Williams continued her dominance through the first week of the U.S. Open and added a piece of history to her name by eliminating Sweden's Johanna Larsson 6-2, 6-1 in her third-round match at New York on Saturday.
Fourth-seeded Agnieszka Radwanska of Poland and fifth-seeded Simona Halep of Romania also won third-round matches, but no one has been as impressive as Williams through the first week.
The win against Larsson was Williams' 307th career victory in Grand Slam events. That total surpassed Martina Navratilova for the most in women's tennis history and tied Roger Federer for the most by any player.
"It was a really good feeling, I have to say," Williams said. "To be up there with both men and women is something that's super rare, and it actually feels good.
"I was really excited to reach that, was it 306? 307? I was really excited to do that. Something I didn't even know about until Wimbledon. I was like, 'Oh, I have a new goal.' That was pretty cool for me. Obviously, I want to keep that number going higher and see what can happen."
Williams has yielded no more than three games in any of the six sets she played in her first three matches, and she has shown no signs of problems from a shoulder injury that plagued her in recent weeks.
"It definitely feels solid," Williams said of her shoulder. "I'm doing a lot of work on it so I can keep it in this position. Definitely not going to stop doing all the rehab and therapy, so I don't want to go down. It's pretty good."
Williams next plays Kazakhstan's Yaroslava Shvedova.
Halep advanced to the round of 16 but had to rally from 3-1 down in the third set to get past 31st-seeded Timea Babos of Hungaria 6-1, 2-6, 6-4.
"It was really tough," Halep said. "She played unbelievable second and third set. She didn't miss at all. She was hitting very strong, so it was a good challenge for me and it was a good match. I'm really proud that I could win it and come back from 3-1 down in the third set."
Halep next plays 11th-seeded of Span, a 6-4, 6-3 winner over 19th-seeded Elena Vesnina of Russia.
Radwanska came into the U.S. Open knowing she could become the world's No. 1-ranked player if certain scenarios played out in her favor.
Radwanska breezed into the fourth round with a 6-2, 6-3 victory over Caroline Garcia. The 25th-seeded Frenchwoman committed 34 unforced errors to help Radwanska win easily.
"I did a good job today from start to the end," said Radwanska, 27. "It was a very solid effort."
Radwanska's fourth-round opponent will be Croatia's Ana Konjuh, who outlasted American Varvara Lepchenko 6-3, 3-6, 6-2.
Sixth-seeded Venus Williams cruised into the fourth round with a 6-1, 6-2 rout of 26th-seeded German Laura Siegemund. Up next for Venus Williams is a match against 10th-seeded Karolina Pliskova. The Czech player knocked out Russia's Anastasia Pavlyuchenkova, the 17th seed, 6-2, 6-4.