King topped eighth-seeded Monica Puig 1-6, 7-5, 7-6 (7-5) in a 2 1/2-hour match that put her one win away from her second WTA finals appearance. She won the Bangkok Open in October 2006.
King dropped her serve seven times, including twice in each of the sets she won. After not managing a break opportunity in the first set, King converted three of four chances in the second and two of three in the third in forcing the match-deciding tiebreaker.
Yvonne Meusburger defeated second-seeded Alize Cornet 6-4, 6-1 for her first win over Cornet since 2007. Meusburger had six breaks and won 61 percent of the points off Cornet's serve. She also saved eight of the 10 break points she faced.
There is chance of all-Chinese final as Zheng Jie and Zhang Shuai both won quarterfinal matches Thursday. Zheng waited out a lengthy rain delay before beating third-seeded Laura Robson 1-6, 7-6 (8-6), 6-2 and Zheng was a 7-5, 6-3 winner over Johanna Konta.
Zheng's upset of Robson meant no seeded players advanced to the semifinals.
She is seeking her seventh WTA final, having won four tournaments, most recently in January 2012. Zhang, a wild-card entrant, is looking for her first WTA final appearance.
Zheng, who faces King in Friday's semis, defeated King last year in Tokyo in their only previous meeting. Meusburger, aiming for her third final of 2013, draws Zhang in the semifinals. Meusburger is 3-1 lifetime against Zhang but Zhang won last year in their most recent meeting.