MELBOURNE, Australia — Just before she walked on court, Greta Arn said she was looking forward to the "privilege" of playing her first match against Serena Williams. Some privilege.
The 13-time Grand Slam champion overpowered Arn 6-1, 6-1 in 59 minutes on Saturday for her 17th straight win at the Australian Open.
The mismatch was so great that the crowd was muted, rousing themselves only when Arn won her two games and when Williams completed her third-round victory.
Arn double-faulted twice to end the match. As the players shook hands at the net, Williams looked briefly taken aback and smiled.
"I told her it was an honor to play against you," the 32-year-old Arn said. "And she told me, 'Oh, you are so sweet.' I'm a big fan of hers. She's the real No. 1."
Williams, who racked up her 501st career match win, is hoping to become the second woman over age 30 to win the Australian title in the Open era.
"It makes me feel really good," she said of her Hungarian opponent's remarks. "I'm really proud of the work that I've been doing for so many years, all the hard work."
Vania King's loss to Ana Ivanovic left Williams as the only American player left in either singles draw. John Isner lost Friday, the last American man to exit.
Coming off an injury-ravaged 18 months, Williams is seeded 12th in Melbourne. She hasn't held the top ranking since 2010, the year she won the last of her Grand Slam titles.
On Saturday, she spoke expansively about her off-court activities: She's taking courses in kinesiology and management and preparing for an appearance in a "pretty big" TV show.
Arn says "everybody knows" if Williams hits top form she will win the Australian Open, where she hasn't lost since 2008. She won back-to-back titles in 2009 and 2010 and was unable to defend her title last year while she recovered from two foot surgeries.
Because of her ranking, Williams can't take the No. 1 spot with a win at Melbourne. However, No. 2 Petra Kvitova, No. 3 Victoria Azarenka and No. 4 Maria Sharapova could walk away with the top ranking if they win the tournament.
Next up for Williams is unseeded Russian Ekaterina Makarova. After that, things are likely to get a lot tougher. Sharapova is a potential quarterfinal opponent, and Wimbledon champion Kvitova may await in the semifinals.
"I'm nowhere near where I want to be," said Williams, who came into the tournament nursing a sprained left ankle. "I'm just trying to play through it. A little rusty, just trying to play through my rust."
Sharapova and Kvitova joined Williams in advancing to the fourth round on Saturday. Between the three of them, they lost six games.
Kvitova was leading 6-0, 1-0 when Russian opponent Maria Kirilenko retired. Sharapova, who won her first two matches 6-0, 6-1, was tested for the first time and still came out with a 6-1, 6-2 win over U.S. Open semifinalist Angelique Kerber.
