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

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).

The 22-year-old Bulgarian, considered one of the up-and-coming players on the men’s tour, held his nerve in a long tiebreaker and is starting to live up to expectations.

“First time for me to be in second week, so I guess I’ll see you guys next week,” No. 22-seeded Dimitrov said.

He has been sometimes referred to as the mini Roger Federer, due their similar styles and single-handed backhands. Even Federer, a 17-time Grand Slam winner, told a news conference after his 6-2, 6-2, 6-3 win over Teymuraz Gabashvili that everyone in the locker room was watching the Dimitrov-Raonic match.

Dimitrov will next play Roberto Bautista Agut, who followed his upset second-round win over No. 5 Juan Martin del Potro with a 6-2, 6-1, 6-4 third-round win over No. 27 Benoit Paire.

Sharapova’s 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 F) conditions she endured for 3 hours, 28 minutes in her second-round win over Karin Knapp two days previously. That encounter 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 — she missed a match point with a wayward backhand on the Frenchwoman’s serve and then got broken twice while trying to serve out.

In the subsequent match on Rod Laver Arena, Federer produced a routine win to follow his detour to Hisense Arena in the second round.

He is seeded sixth at this Australian Open, his lowest seeding in more than a decade, after a year in which he didn’t reach a Grand Slam final for the first time since 2002. His wife, Mirka, and their twin daughters were in the arena watching against 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.”

Sharapova will next play Dominika Cibulkova, who beat No. 16 Carla Suarez Navarro 6-1, 6-0 in 59 minutes. Suarez Navarro was clearly still fatigued from her three-hour, second-round match in the extreme heat. She hit only two winners against Cibulkova.

“I finished the last match with pain. I tried to recover yesterday but it was not possible to play good today,” she said after Saturday’s defeat. “When you play with these players at this level, you need to be 90 percent perfect or 100 percent perfect. If you are less than this, you cannot play, you cannot be on court.”

Former No. 1-ranked Jelena Jankovic had a 6-4,7-5 win over Kurumi Nara, her third consecutive victory over a Japanese player, to set up a fourth-round match against No. 11 Simona Halep, who advanced with a 6-1, 6-4 over qualifier Zarina Diyas. Fifth-seeded Agnieszka Radwanska had a 5-7, 6-2, 6-2 over No. 29 Anastasia Pavlyuchenkova.

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. She will play either two-time defending champion Victoria Azarenka or Yvonne Meusburger in the next round.