Kuznetsova, seeded eighth, ousted No 2-seeded Roberta Vinci 6-2, 6-3 with two breaks in the first set and four in the second. Kuznetsova dropped only two points on serve in the first set. She won barely more than half -- 25-of-49 points -- on serve in the second but the four breaks sealed the win.
Stosur, the No. 7 seed, came out on top of a 7-5, 6-4 match against fourth-seeded Ana Ivanovic. Stosur lost her serve once but claimed 70 percent of the points on serve.
No. 5-seeded Simona Halep had no trouble in a 6-1, 6-1 win over Alisa Kleybanova. Halep had five breaks in seven receiving games while losing only 10 points over seven games serving.
Stosur and Kuznetsova are to play in the first semifinal Saturday. They have split their first six meetings 3-3 although Stosur has won both of their matches in 2013. Halep takes a 2-0 career edge over Pavlyuchenkova into their semifinal.