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.
The 13-time Grand Slam champion overpowered Arn 6-1, 6-1 in 59 minutes 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 back 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.
Azarenka was an early winner on Sunday, beating Iveta Benesova 6-2, 6-2 to become the first player to reach the quarterfinals.
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.
Like Williams, Sharapova came into the tournament short of matches. The three-time Grand Slam champion hurt her left ankle late last season and didn't play a tuneup event before the Australian Open.
"Whether it's a Grand Slam or anywhere else in the world, if you're committed to playing that tournament you have to be ready from the first match," Sharapova said.
It was a day of lopsided scorelines on Rod Laver Arena.
No. 1-ranked Novak Djokovic routed Nicolas Mahut 6-0, 6-1, 6-1 in 1 hour, 14 minutes to give the Frenchman a lousy 30th birthday present.
Mahut, who lost the longest Grand Slam match in history at 11 hours, 5 minutes at Wimbledon in 2010, was hampered by a left leg injury, but said he played because the previous matches on Rod Laver Arena were over so quickly.
"I wish him happy birthday and hopefully tonight he can enjoy it," Djokovic said.
The defending champion has won 24 straight sets at the Australian Open, and has lost 10 games in his first three matches this time.
"I always played well in Australia. This is the only Grand Slam I won twice," he said. "The conditions are great. They're very suitable to my style of the game, day and night. I'm really looking forward to next week."
Djokovic likely gets an evening slot for his fourth-round match against Lleyton Hewitt. The 30-year-old Australian downed promising Canadian Milos Raonic 4-6, 6-3, 7-6 (5), 6-3 in Saturday's final match of the day before a raucous home crowd.
Playing in his 16th straight Australian Open, Hewitt needed three match points in the final game to close out the win and become the first wild card entry to reach the fourth round in Melbourne since Mats Wilander in 1994.
"It's just a game," Hewitt said. "But it's a bloody big game."
No. 2-ranked Rafael Nadal and No. 3 Roger Federer are back on court in a Sunday schedule that features a repeat of the 2011 women's final between Kim Clijsters and Li Na. Federer is up against Australian teenager Bernard Tomic. Nadal faces fellow Spaniard Felicano Lopez.
No. 4-ranked Andy Murray, beaten in the last two Australian finals, brushed aside Michael Llodra 6-4, 6-2, 6-0 Saturday to leave France with two players in the draw, having started the day with six.
Jo-Wilfried Tsonga was the other Frenchman to advance. The 2008 finalist beat Frederico Gil of Portugal 6-2, 6-2, 6-2.
He will play Kei Nishikori, the first Japanese man to reach the fourth round in Melbourne in the Open era. Mikhail Kukushkin, who beat an ailing Gael Monfils in five sets, will be the first man from Kazakhstan to play a round of 16 match at a Grand Slam when he faces Murray.
Williams is frequently the only American left in a tournament, and it doesn't bother her.
"I really don't think when I go out there that I'm the last American," she said. "I just think I'm trying to come in here and win this match, play this girl. That's all I really think about."