DOHA: Serena Williams advanced first into the semi-finals 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 needs Kuzne-tsova to beat Dementieva to have a chance of advancing from 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 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!” Serena, who secured the year-end No 1 ranking after Safina retired with a back injury, has failed to get out of the round-robin phase of the elite tournament for the last two years.

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. Venus dominated the first set but again struggled to put the match away, after wasting a one-set lead in both her previous matches. The Williams sisters are also playing in the four-team doubles tournament, with the semi-finals 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 US Open finalist’s second win in the tournament, putting her on the verge of the semi-finals. 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.