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Sharapova, Federer both into 4th round

Roger Federer took a 6-2, 6-2, 6-3 victory over Teymuraz Gabashvili in the third round of the Australian Open and will meet the Jo-Wilfried Tsonga-Gilles Simon winner. david crosling/epa

MELBOURNE — Maria Sharapova recovered from the longest, hottest match of her career to beat Alize Cornet, 6-1, 7-6 (8-6), Saturday and reach the fourth round of the Australian Open.

Her third-round match was played in high humidity but in temperatures of about 72 degrees, considerably cooler than the scorching 108 conditions she endured for 3 hours and 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 — she missed a match point with a wayward backhand on the Frenchwoman’s serve, then got broken twice while trying to serve out.

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In the next match at Rod Laver Arena, Roger Federer — after a detour to Hisense Arena in the second round — had a 6-2, 6-2, 6-3 win over Teymuraz Gabashvili.

He is seeded sixth 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. 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.’’

Federer will next meet either 2008 finalist Jo-Wilfried Tsonga or No. 18 Gilles Simon.

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 35 unforced errors in the second set after breezing through the first against Cornet.

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‘‘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.

‘‘Everyone that played a long match in those conditions is going to feel physically and emotionally tired, and that’s the way it goes. You just have to find a way to get through it . . . that’s what I did.’’

No. 25 Cornet appeared to be laboring between points in the second set, spending time retreating to the shade and breathing deeply at certain stages. She had been clearly distressed after her second-round win in the heat, which she described as like ‘‘an oven.’’

Sharapova will 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.’’

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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 win over No. 29 Anastasia Pavlyuchenkova.

No. 13 Sloane Stephens reached the fourth round at a fifth consecutive major with a 7-5, 6-4 win over Elina Svitolina of the Ukraine. She will play either two-time defending champion Victoria Azarenka or Yvonne Meusburger in the next round.