After going up 5-4 in the first set, Allertova won six of the next seven games for a 5-1 lead in the second and then closed the match out with a backhand winner.
"I have amazing feelings because I won against Simona Halep -- she's a great player, ranked No. 2. I can breathe now!" Allertova told the WTA website after the match.
"I don't know, I was just trying to focus every point, not looking who's on the other side, just focusing on myself and playing my tennis. I was fighting every point and it worked. I'm so happy.
"It was my first time playing such a top player like this, but at the U.S. Open I played against Suárez Navarro, also an amazing player, a top 10 player, and I beat her, but it's the first time in my life to have a win like this."
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Unseeded Yanina Wickmayer of Belgium earlier defeated another Romanian in sixth seed Monica Niculescu 6-2 6-2 while third-seeded Sara Errani powered past local hope Zheng Saisai 6-1 6-0 for a semi-final meeting with Allertova.
Number four seed Jelena Jankovic of Serbia also reached the last four by defeating fifth-seeded Russian Svetlana Kuznetsova 6-2 7-5.
(Writing by Sudipto Ganguly in Mumbai,; editing by Pritha Sarkar)
