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Peng was two points from victory at 64 65, 30-30 on Martic's serve, but the Croat rallied to take the second set in a tie-break and then in the third broke Peng's serve at 5-4 to clinch the 46 76(3) 64 triumph.
Martic is now 3-1 in her last four quarterfinals and is into her third final four, having also gotten that far last year in Bogotá and Copenhagen. She also bagged her second career Top 20 win, as after topping No.15 Yanina Wickmayer at Paris [Indoors] in 2010, she had lost 10 straight versus Top 20 players until defeating the 19th-ranked Peng.
"It is a great feeling to beat a Top 20 player after so long," Martic said. "I took advice from my coach, who told me to play the game on a point-by-point basis and not to think of the outcome of the match.
"I'm happy. This is probably the one time I've been so aggressive and it worked."
The only other player to secure a semifinal berth was qualifier Hsieh Su-Wei, who advanced by walkover because of an elbow injury suffered by No.1 seed Agnieszka Radwanska. Hsieh made the final four of her first-ever WTA event at Bali in 2001 and then did not make another until last month in Pattaya City. Now in her very next event, she is into yet another.
"I haven't paid much attention to who I'm playing next before this but now I can," Hsieh saud. "It would be interesting to play Eleni Daniilidou of Greece. It has been a long time since I played her."
However, Daniilidou still has some work to do to ensure that clash, as she was up on Olivia Rogowska, 62 32, and was serving at 0-40 when the match was suspended. Second-seeded Jelena Jankovic and sixth-seeded Ayumi Morita did not even take the court, so the winner of that will have to play two full matches on semifinal Saturday.
Advancing to the doubles semifinals against No.3 seeds Hao-Ching Chan and Rika Fujiwara were Czechs Karolina and Kristyna Pliskova. The other semi will see Australian No.1 seeds Casey Dellacqua and Jarmila Gajdosova square off with Chang Kai-Chen and Chuang Chia-Jung.