Maria Sharapova beats Rebecca Peterson 6-2, 6-1 to move on to the third round of the Australian Open. (0:43)

Maria Sharapova set up a third-round showdown with defending champion Caroline Wozniacki at the Australian Open after a 6-2, 6-1 win over Rebecca Peterson of Sweden.

The Russian has dropped only three games in her first two matches and is hitting form quickly despite sitting out the end of the 2018 season to give her right shoulder a rest after a fourth-round exit at the US Open.

The third-seeded Wozniacki also beat a Swedish opponent in the second round, advancing 6-1, 6-3 over Johanna Larsson.

Wozniacki's match was considerably earlier in the day, while Sharapova's win wrapped up Day 3 after midnight Thursday.

"I don't know about you guys, but this is way past my bedtime," Sharapova told the crowd at Margaret Court Arena. "I'm just thinking what time I'm going to get to sleep."

Sharapova won the Australian title in 2008, has reached the final at Melbourne Park three other times and can raise her game well above the status of a No. 30 seed.

In a second-round match, the women's tour billed as a battle of "frenemies," Sloane Stephens advanced at the expense of her former doubles partner Timea Babos.

Fifth-seeded Stephens, the 2017 US Open champion, dominated the Rod Laver Arena opener 6-3, 6-1 on Wednesday, but Babos kept her working by saving 18 of the 23 break points she faced.

This is the first time since 2014 that Stephens has put back-to-back wins together at Melbourne Park. She reached the fourth round in 2014, a year after making a run to the semifinals.

She puts the improvement down to feeling more relaxed.

"Yeah, considering I haven't won a match here in I don't know how long,'' she said. "I'm kind of conquering all the places where I've been terrible. So Asia, I've won a few matches there, and here.

"I know I haven't done well here the last few years ... [so] putting the emphasis on trying to start the year on a good foot."

Stephens and Babos combined to win three junior Grand Slam doubles titles -- the French, Wimbledon and US Open -- in 2010.

Stephens couldn't remember exactly how the combination was formed in the juniors but said she knew what to expect from Babos.

"She obviously is an incredible doubles player, last year No. 1 in the world,'' she said. "I see her every week. We're good."

Stephens will next play No. 31-seeded Petra Martic, who beat Marketa Vondrousova 6-4, 7-5.

In other matches Wednesday, Ashleigh Barty had seven aces and dropped serve only once in a 6-2, 6-3 win over Yafan Wang to continue her bid to end a title drought for Australian women at the championship that dates to 1978.

Barty said after her win that her coach Craig Tyzzer is bedridden and that she is getting help in the meantime from Australian Fed Cup coach Alicia Molik.

Sloane Stephens bested former junior doubles partner Timea Babos 6-3, 6-1 to reach the third round of the Australian Open on Wednesday. Lukas Coch/EPA

"He's on bed rest at the moment,'' Barty said of Tyzzer. "Extremely lucky to have a Fed Cup captain in [Molik], who ... is also around a lot of the slams. It's a very seamless transition."

Barty said she was still communicating with Tyzzer by phone.

Australian wild-card entry Kimberly Birrell upset No. 29-seeded Donna Vekic 6-4, 4-6, 6-1 to reach the third round.

"It is so surreal," the 20-year-old, No. 240-ranked Birrell said. "That was just such a blur. I get to play again. It's crazy."

Next up for Birrell is Angelique Kerber, who won her match against Beatriz Haddad Maia 6-2, 6-3. The first set took 47 minutes thanks to a marathon sixth game with Haddad Maia serving. It went nearly 14 minutes with 10 deuces, and Kerber had six break points that were saved by the Brazilian qualifier.

American teenager Amanda Anisimova advanced to the third round with a 6-0, 6-2 win over 24th-seeded Lesia Tsurenko.

Tsurenko, a finalist at the Brisbane International two weeks ago, had only nine winners in the 54-minute match.

Anisimova, 17, born in New Jersey to Russian-born parents, is ranked 92nd and is the youngest of all players currently ranked in the top 100.

Anastasia Pavlyuchenkova eliminated ninth-seeded Kiki Bertens 3-6, 6-3, 6-3 to reach the third round of a major for the first time since her quarterfinal run here in 2017, and Aliaksandra Sasnovich beat 20th-seeded Anett Kontaveit 6-3, 6-3.

No. 11 seed Aryna Sabalenka and No. 19-seeded Caroline Garcia both won their matches in straight sets.

No. 8 seed Petra Kvitova, the two-time Wimbledon champion, reached the third round with a 6-1, 6-3 victory over Irina-Camelia Begu.

The Associated Press contributed to this report.