Hingis, the second seed from Switzerland, defeated seventh seed Sandrine Testud of France, 6-4, 6-2, while Clijsters, the third seed, outlasted fifth-seed Justine Henin, 7-6 (7-5), 6-2, in a
battle of players from Belgium.
Friday's semifinal will feature Hingis seeking her 500th professional singles victory. Clijsters will earn her 200th winif she can defeat Hingis.
Eighth seed Meghann Shaughnessy moved into the semifinals by topping fellow American Alexandra Stevenson, 6-4, 6-1.
Stevenson had ousted defending Australian Open champion Jennifer Capriati on Wednesday.
In men's quarterfinal action, second seed Roger Federer of Switzerland outlasted Chile's Marcelo Rios, 6-7 (2-7), 7-6 (7-4), 6-3. Federer advances to play third-seeded Andy Roddick of the United States, who defeated Hyung-Taik Lee of Korea, 6-7
(3-7), 6-3, 7-5.
Qualifier Juan Ignacio Chela of Argentina moved into the final in a walkover. Nicolas Escude, who was instrumental in France's Davis Cup victoy over Australia in last month's final, was unable to play due to a groin injury.
Max Mirnyi of Belarus topped France's Juilen Boutter, 6-4, 6-2, in a battle of unseeded players.
Celebrity Families of 2014 [PHOTOS]