Video: Williams and Wozniacki through to the semi-finals in Japan

Williams joins fourth seed Caroline Wozniacki in the next round after the Dane defeated Lucie Safarova 2-6, 6- 3, 6-2 – Wozniacki will now play fifth-seed Angelique Kerber of Germany in the last four after the German ousted second-seeded Agnieszka Radwanska of Poland 6-4, 6-4.

Seventh seed Petra Kvitova eased into the quarter-finals of Toray Pan Pacific Open on Thursday (26th September) with a straight sets 6-2, 6-2 win over 18-year-old American Madison Keys.The 23-year-old took an hour and 15 minutes to wrap up the match and will now face Russian Svetlana Kuznetsova in the last eight.

Kuznetsova, a former US Open and French Open champion, was taken to a tie-break in the first set of her third round contest against Romanian Sorana Cirstea but won it 7-3.

Cirstea folded after that and 28-year-old Kuznetsova, who is ranked 27th in the world, won the second set 6-1 to advance in straight sets.

Venus Williams beat Canadian teenager Eugenie Bouchard 6-3, 6-7 (4-7), 6-3 to advance to the semi-finals for the first time.

The unseeded former world number one and seven-time Grand Slam champion, whose previous best in Tokyo was the quarter-finals in 2004, broke Bouchard with a forehand down the line to go up 5-2 in the third set – and then held on to win a match that lasted three hours.

Williams will now face either Svetlana Kuznetsova or Petra Kvitova in the semis.

It was also a relatively easy contest for Caroline Wozniacki in her quarter-final.

The fourth seed defeated Lucie Safarova 6-1, 6-1 to gain a straightforward progression into the last four.

Wozniacki will meet fifth-seed Angelique Kerber of Germany in the semi-final stage, after the German defeated second-seed Agnieszka Radwanska.

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