NEW YORK — Serena Williams had an image in mind when she designed her current tennis outfit. The fluorescent pink sleeves, she said, make her think of the superhero characters Wonder Woman and Superwoman.
It is an appropriate image for one of the greatest tennis players of all time, a player seemingly without peer as she topples one record after another.
Williams explained that the design of her sleeves — she wears black ones for night matches — was intended to evoke a character of power and strength who is also unafraid to exhibit a softer side.
There was little question of who she had in mind, although she acknowledged, with a satisfied nod, “It is me.’’
With her 6-2, 6-1 victory Saturday over Johanna Larsson in the third round of the US Open, Williams earned her 307th victory in Grand Slam singles events. That carries her past Martina Navratilova for most by a woman, and ties her with Roger Federer for the most by any player.
Seeded No. 1, Williams is one trophy away from winning her 23d Grand Slam singles title, which would break a tie with Steffi Graf for the most championships in the Open era. (Margaret Court won 24 in a career that spanned both the amateur and Open eras.)
If Williams wins this tournament, she will break a tie with Chris Evert for the most US Open titles by claiming her seventh.
Williams said she had first learned at Wimbledon that she was close to passing Navratilova, and it had given her a new goal.
“It is actually a really good feeling,’’ she said Saturday. “To be up there with both men and women is something that’s super rare.’’
Two past men’s champions, Andy Murray and Juan Martin del Potro, moved into the fourth round.
Murray took a 7-6 (7-4), 5-7, 6-2, 6-3 victory over Paolo Lorenzi. Dan Evans of Britain faded in a 4-6, 6-3, 6-7 (6-8), 7-6 (8-6), 6-2 loss to No. 3 Stan Wawrinka.
There’s only one American man left: Jack Sock, who faces No. 9 Jo-Wilfried Tsonga on Sunday. That’s because 19-year-old qualifier Jared Donaldson’s run ended with a straight-set loss to 37-year-old Ivo Karlovic, the oldest man to reach the fourth round in New York since Jimmy Connors was 39 in 1991. Karlovic plays No. 6 Kei Nishikori next.
Serena’s next victory would push her past Federer’s total, likely generating more discussion about whether Williams is one of the best athletes, male or female, of all time.
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 52d-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 No. 5 seed Simona Halep, a 6-1, 2-6, 6-4 winner over No. 31 seed Timea Babos. Halep will play the No. 11 seed Carla Suárez Navarro in the fourth round.
Agnieszka Radwanska, the No. 4 seed, beat Caroline Garcia, 6-2, 6-3, and could be headed for a quarterfinal matchup with No. 6 seed Venus Williams, who defeated Laura Siegemund, 6-1, 6-2, in Arthur Ashe Stadium Saturday night.
All of them have aspirations to win the tournament, but with Serena Williams effortlessly blazing through the draw so far (losing only 15 games), the others have a considerable challenge to overcome.
There were some concerns about Serena’s sore right shoulder. But she says it is improving every day. Her fastest serve Saturday was 121 miles per hour, and she saved the only break point she faced against Larsson.
Still, Serena Williams said she was not quite at her best.
“I don’t feel like I’m Serena out there yet,’’ she said. “But hopefully she’ll come around the second week.’’
She might come wearing a cape.
