Maria Sharapova holds on, advances MELBOURNE, Australia -- Maria Sharapova recovered from the longest, hottest match of her career to beat Alize Cornet 6-1, 7-6 (6) on 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 Fahrenheit, considerably cooler than the scorching 108-degree conditions she endured for 3 hours, 28 minutes in her second-round win over Karin Knapp two days previously. The tournament's extreme heat policy was enacted for the first time in five years during that match. Again, though, Sharapova struggled to close out Saturday. 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. Sharapova is slowing finding her groove in her second tournament back after a prolonged break for a right shoulder injury. "After the last match, I'm just happy to get through this," Sharapova said. 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. The third-seeded Sharapova was still wearing ice vests and draping ice-filled towels over her shoulders in the changeovers Saturday. 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, sobbing when she described the conditions as like "an oven." Suarez Navarro was clearly still fatigued from her 3-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. American Sloane Stephens advanced to the fourth round with a 7-5, 6-4 win over Elina Svitolina of Ukraine. Last year, Stephens made it to the fourth round or better at all four majors -- joining Serena Williams and Agnieszka Radwanska as the only players to achieve that feat. And Stephens, seeded 13th this year, beat Williams in last year's quarterfinals at Melbourne Park, one of only four losses for Williams in 2013. Stephens, 20, who has never lost to an opponent ranked lower than her in a Grand Slam event, will play either two-time defending champion Victoria Azarenka or Yvonne Meusburger in the next round. 1-ranked Jelena Jankovic had a 6-4,7-5 win over Kurumi Nara 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 Radwanska had a 5-7, 6-2, 6-2 win over No. 29 Anastasia Pavlyuchenkova and will next play Garbine Muguruza Blanco of Spain, who beat former No. 1-ranked Caroline Wozniacki 4-6, 7-5, 6-3. Wozniacki now will have to wait until at least the French Open to claim an elusive first Grand Slam title. Muguruza Blanco won her first WTA tournament two weeks ago at the Hobart International.