MELBOURNE, Australia -- Maria Sharapova recovered from the longest, hottest match of her career to beat Alize Cornet 6-1, 7-6 (6) on Saturday (Australia time) to reach the fourth round of the Australian Open.

Her third-round match was played in high humidity but in temperatures of about 22 Celsius (72 Fahrenheit), considerably cooler than the scorching 42 C (108 degees F) conditions she endured for 3 hours, 28 minutes in her second-round win over Karin Knapp two days previously. That preceded the first match suspensions under the tournament's Extreme Heat Policy in five years.

Again, though, Sharapova struggled to close out. She took 50 minutes between her first and last match points against Knapp, and needed almost a half-hour to finish off Cornet.

Sharapova's boyfriend, Grigor Dimitrov, progressed to the second week at a major for the first time when he converted his fifth match point to beat No. 11-seeded Milos Raonic of Canada 6-3, 3-6, 6-4, 7-6 (10).

No. 13 Sloane Stephens, who had an upset win over Serena Williams in the quarterfinals here last year, reached the fourth round at a fifth consecutive major with a 7-5, 6-4 win over Elina Svitolina of Ukraine.

No. 10 Caroline Wozniacki will have to wait to claim an elusive first Grand Slam title after being beaten 4-6, 7-5, 6-3 by Garbine Muguruza in the third round.

On the men's side, Roger Federer, the sixth seed, and fourth-seeded Andy Murray cruised in straight sets into the fourth round.

Federer didn't reach a Grand Slam final last year for the first time since 2002. His wife, Mirka, and their twin daughters were in the arena watching against Teymuraz Gabashvili. The couple is expecting another child later in the year, something Federer sees as a good omen.

"The last time (Mirka) was pregnant I played fairly well, won the French and Wimbledon" he said, in reference to 2009. "So lots of pressure there."

Sharapova is slowing finding her groove in her second tournament back after a prolonged break for a right shoulder injury. She had six double-faults and 29 of her total 35 unforced errors in the second set after breezing through the first against Cornet.

"After the last match I'm just happy to get through this," Sharapova said. "Definitely need to step it up. I was lucky to get through the other day, now that I'm in the second week, I'm level."

The four-time major winner needed an ice bath after her second-round win but joked about needing a warm bath following her victory over Cornet.

"It's such a quick change," Sharapova said of the cooler conditions. "I think it's really welcome from all of us."

Sharapova will next play Dominika Cibulkova, who beat No. 16 Carla Suarez Navarro 6-1, 6-0.