In a strong performance, Williams broke the eighth-seeded Stosur's serve four times.
Williams, who will climb to the second ranking behind sister Serena next week, has now won all four of her meetings with the Australian.
She plays either Shahar Peer or Li Na in the semi-finals.
Despite the defeat, Stosur's recent form is projected to send her to seventh in the rankings next week, the highest held by an Australian since Wendy Turnbull in 1985.
Earlier, Lucie Safarova progressed to the semi-finals with a 6-1, 1-6, 6-4 victory over 16th-seeded Nadia Petrova.
Safarova has had a fine clay-court season, reaching the quarterfinals in Stuttgart and Rome and she will next face either seventh-seeded Jelena Jankovic or Aravane Rezai.
In the men's tournament, Spain's Nicolas Almagro reached his first ATP Masters semi-final by beating Jurgen Melzer 6-3, 6-1.
In the only quarterfinal not to feature a seeded player, Almagro broke Melzer twice to close out the first set before racing to a 3-0 lead in the second with some solid serving.
The 24-year-old had another break before securing a semi-final against the winner of the match between Gael Monfils and Rafael Nadal in the semi-finals.