Venus Williams earned her first victory of the season-ending tournament

Venus Williams beat Svetlana Kuznetsova to keep alive her hopes of making it through to the semi-finals of the Sony Ericsson Championships in Doha.

Williams beat her Russian opponent 6-2 6-7 (3-7) 6-4 to earn her first win in the round-robin season-ending event.

Venus, with one win out of three, must now hope Kuznetsova beats Elena Dementieva on Friday to have a chance.

Earlier, world number one Serena Williams booked her semi-final place, while Caroline Wozniacki edged closer.

Defending champion Venus Williams eased through the first set in impressive fashion against Kuznetsova but was beaten in a well contested second set on a tie-break.

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However, Williams battled back and broke her opponent in the third game of the final set to earn an early advantage in the decider.

Although the American herself was broken in the sixth game, she broke Kuznetsova two games later and served out for the match.

"Svetlana just started to play really well in the second and third set," said Venus. "It's always great to win these kinds of matches."

Also in the Maroon Group, Serena Williams cruised into the semi-finals by beating Dementieva 6-2 6-4 for her third straight win in the group phase.

The second seed was broken to trail 2-1 in the first set but then won seven straight games to take control of the match. She converted her third match point when Dementieva sent the ball into the net.

"It was definitely a match I had to be really focused for, because she's a really good player," said Serena.

"She's one of those late bloomers who tends to get better and better as every year goes on in her career. I was probably playing the fittest girl on tour."

Caroline Wozniacki suffered cramp in her match

In the White Group, Danish teenager Wozniacki overcame crippling cramp to defeat Russia's late call-up Vera Zvonareva 6-0 6-7 (3-7) 6-4 in a classic encounter.

The 25-year-old Zvonareva battled impressively, even overcoming a nasty courtside nose bleed in the second set.

But Wozniacki ended the two hour, 48-minute match in floods of tears after collapsing to the court in agony, clasping her left thigh, when she was just two points from victory.

"I have absolutely no idea how I pulled it through, but I'm very happy about it," said Wozniacki.

Wozniacki said her leg started cramping at 3-1 in the third set.

"From there, it just got worse and worse," she said. "I'm feeling better now. I got to cool down, getting some massage. I'm going to do everything tonight to recover to be ready for Friday."

She added: "I'm just going to do everything that physio and the doctors are saying, drinking a lot of fluids, eat some good food, stretch, get some massage, get some ice massage, take a salt bath, everything."

World number nine Zvonareva, who was summoned to the £2.8m event after Dinara Safina pulled out on Wednesday, later withdrew with an ankle injury.

Second reserve Agnieszka Radwanska of Poland will now get a run out against semi-final hopeful Victoria Azarenka on Friday.

The season finale is split into two groups of four, with the top two in each group making the semi-finals and the eventual champion taking home (£944,000).

Friday's order of play:

1. Caroline Wozniacki v Jelena Jankovic
2. Svetlana Kuznetsova v Elena Dementieva
3. Agnieszka Radwanska v Victoria Azarenka

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