KEY BISCAYNE, Fla. -- Mired in a marathon game midway through the opening set, Maria Sharapova wore down her opponent with characteristic resolve and relentlessness, winning the last point without hitting a shot.
That put Sharapova ahead to stay, and she beat fellow Russian Elena Vesnina on a muggy, 85-degree afternoon at the Sony Open, 6-4, 6-2.
The No. 3-seeded Sharapova moved into the fourth round, eager to fill one of the few holes in her resume. While she completed a career Grand Slam last year, she has never won Key Biscayne, losing the final in 2005, '06, '11 and '12.
"It's in the back of my mind," she said. "It's one of the biggest tournaments for us, and it's one that I have been the most consistent at, being in four finals, but yet not winning it. I would definitely love to go a step further here."
Her pivotal moment Sunday came at 3-all in the first set. The next game went to deuce seven times, with Sharapova repeatedly erasing a deficit, until Vesnina dumped a weary second serve into the net on break point.
"That was a very important game," Sharapova said. "It was a really long one. I was ready for a water break."
All told, Sharapova benefited from eight double-faults by the No. 29-seeded Vesnina, and erased eight of the nine break points she faced.
Lauren Davis of the United States lost to No. 32-seeded Alize Cornet at the peak of the heat, and their 2½-hour match left both players so exhausted they were taken off the court in wheelchairs. Davis also required treatment in the third set after being stung by a wasp.
Both players later said they were fine. Cornet won 2-6, 6-3, 6-2.
Top-ranked Novak Djokovic, seeking his fourth Key Biscayne title and third in a row, defeated No. 254-ranked Somdev Devvarman 6-2, 6-4. Djokovic next faces No. 15-seeded Tommy Haas, who beat No. 19 Alexandr Dolgopolov 6-3, 6-2.
Haas turns 35 next month and is playing at Key Biscayne for the 12th time.
"You can always expect Tommy to fight and try his best," Djokovic said. "So I know what to expect. It's going to be a tough match."
Among the seeded women to lose were No. 6 Angelique Kerber, No. 11 Nadia Petrova and No. 14 Maria Kirilenko. Kerber was beaten by No. 28 Sorana Cirstea 6-4, 6-0. Petrova was ousted by No. 22 Jelena Jankovic 7-6 (7), 6-4. Kirilenko lost to No. 21 Klara Zakopalova 6-2, 7-6 (4).
The sweltering sunshine was motivation to work quickly, but Sharapova needed nearly two hours to eliminate Vesnina. Both players struggled with their serve as they battled the island breeze, and both rued missed chances. Sharapova converted only four of 18 break points.
When Vesnina finally sailed a shot long to lose the opening set, Sharapova screamed and shook her fist at the ball, as though trying to intimidate it. The gesture seemed to work, and she claimed the second set more easily.
"It was a matter of patience," Sharapova said. "In situations like this where it's tough and it's hot, it kind of levels out the game a little bit, and with the windy conditions you have to be a bit more patient. That was really important today."
Vesnina fell to 1-18 against top-five players.
Sharapova seeks to become only the third woman to win Indian Wells and Key Biscayne back to back. She beat Caroline Wozniacki in the Indian Wells final a week ago and has a record of 16-2 this year.
She has lost Key Biscayne finals to Kim Clijsters, Svetlana Kuznetsova, Victoria Azarenka and Agnieszka Radwanska. Her history at the tournament actually dates back even further -- to grade school, when her family lived Bradenton, Fla., and would attend matches as spectators.
"It was just a four-hour drive down," she said. "We'd watch Yevgeny Kafelnikov, and I remember watching Marcelo Rios playing. I loved watching him play, and especially all the Latin fans at close to midnight still going strong. It was a great atmosphere.
"I was a fan, and now I'm a player here."
But not yet a champion. Top-ranked Serena Williams looms as a potential opponent in Saturday's final.