Her next victory, which would push her past Federer’s total, would most likely generate more discussion about whether Williams is one of the best athletes, male or female, of all time. She welcomes the debate.

On Saturday, Williams expended almost as much energy playing advocate as she did in her hourlong win over Larsson. Williams argued that disparities persisted between the way male and female athletes were perceived and paid.

“I definitely think there is a difference between the way male and female athletes are treated,” she said. “I also believe that as a woman, we have still a lot to do and a lot to be going forward.”

Williams noted that female tennis players had been at the forefront of trying to achieve equality in their sport, and she said it was important for them to push for similar conditions for other female athletes.

“Tennis players were really fortunate to have pioneers like Billie Jean King and really take a stance for women in tennis,” Williams said. “I feel like we got really, really fortunate to have that. So now we’re able to benefit and still preach the message and have an easier time. Hopefully, that can work out for other females, as well.”

With her superhero sleeves and dominating performances, Williams may not be helpful to the other women in her draw when she is on court. In the fourth round, Williams will play the 52nd-ranked Yaroslava Shvedova of Kazakhstan, who beat Shuai Zhang, 6-2, 7-5.

A victory by Williams in the next round could set up a quarterfinal match against the No. 5 seed Simona Halep, who faced a stern challenge Saturday from the No. 31 seed Timea Babos. Halep held on to win an emotional match, 6-1, 2-6, 6-4, and she will play the No. 11 seed Carla Suárez Navarro in the fourth round. The two have evenly split their 10 previous matches.