She griped about the challenging conditions, but still recorded a 6-1, 7-5 victory over France's Nathalie Dechy.
Capriati will take on defending champion Chanda Rubin of the United States. The second seed hammered Israeli Anna Pistolesi, 6-1, 6-0.
"It was hard to concentrate in the conditions," said Capriati, a three-time Grand Slam champion who is without a tournament victory since the 2002 Australian Open. "It was so difficult out there. It's hard to call this tennis."
Spain's Conchita Martinez also reached the semifinals, defeating fourth seed Daniela Hantuchova of Slovakia, 6-2, 6-3.
Martinez will face veteran Silvia Farina Elia of Italy, who rallied past eighth seed Magdalena Maleeva of Bulgaria, 5-7, 6-4, 6-4.