Serena Williams advanced first into the semifinals of the Sony Ericsson Championships after beating Elena Dementieva 6-2, 6-4 for her third straight win in the group phase on Thursday.

Her sister Venus, the defending champion, also stayed alive by beating Svetlana Kuznetsova 6-2, 6-7 (3), 6-4 for her first win in three matches. She still needs Kuznetsova to beat Dementieva on Friday to have a chance of advancing from the Maroon Group.

In the White Group, Caroline Wozniacki overcame severe leg cramps and a tenacious Vera Zvonareva to win 6-0, 6-7 (3), 6-4. Zvonareva, who replaced injured No. 1 Dinara Safina on Wednesday, then pulled out the tournament citing a right ankle injury. Her place will be taken by the second alternate, Agnieszka Radwanska of Poland, who will play Victoria Azarenka on Friday but has no chance of advancing.

Serena was broken to trail 2-1 in the first set but then won seven straight games to take control of the match, moving Dementieva around the court with her powerful ground strokes.

She converted her third match point when Dementieva sent the ball into the net, then pumped her fist and yelled “Finally!”

“I’m happy to finally do well,” she said. “I’m kind of used to the elimination thing: If you lose, you’re out. But I was just trying to do better than I did last year, and compete in all my matches, which sometimes is very hard.”

Dementieva, who rallied from a set down to beat Venus in their opening match, didn’t find her stride against Serena until trailing 2-0 in the second set, as the encounter failed to live up to their epic three-set Wimbledon semifinal - billed by many as the best women’s match of the year.

Dementieva won the longest game of the match after converting her fifth break point to make it 2-1, and the set went with serve until the last game.

Venus, who lost another three-setter to Serena on Thursday, broke Kuznetsova at love for a 5-4 lead in the third set and then converted her third match point when the Russian’s backhand landed in the net shortly before 1 a.m. local time.

Venus dominated the first set but again struggled to put the match away, after wasting a one-set lead in both her previous matches. “Svetlana just started to play really well in the second and third set,” she said. “It’s always great to win these kinds of matches.”

The Williams sisters are also playing in the four-team doubles tournament, with the semifinals on Saturday.

Wozniacki needed two medical time-outs to treat her cramping left thigh in the third set and collapsed to the court sobbing and clutching both legs after netting a forehand at 30-15 in the last game. But she got back up and clinched the win when Zvonareva, who had saved two match points in the second set, netted a forehand on the third.

“I have absolutely no idea how I pulled it through, but I’m very happy about it,” Wozniacki said.

It was the U.S. Open finalist’s second win in the tournament, putting her on the verge of the semifinals.

At 3-2 in the second set, Zvonareva needed a five-minute medical time-out to treat a bleeding nose, and the match looked headed for a quick finish after she lost the next two games at love.

However, Zvonareva won the next three games and saved two match points when serving at 5-6 - the first thanks to a Hawkeye challenge after a line judge ruled that her forehand had gone wide.

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