Vinci, seeded fifth, ousted No. 3-seeded Yanina Wickmayer 6-4, 6-4 despite landing less than half of her first serves. Even with the serving problems, Vinci dropped serve just twice while getting four breaks in Wickmayer's 10 service games.
She won't learn her semifinal opponent until Friday however, as rain caused a suspension of a match between second-seeded Svetlana Kuznetsova and No. 5-seeded Dominika Cibulkova. Cibulkova has a 3-0 lead in the third set.
Three men's quarterfinals at the UNICEF Open were also unable to finish because of the rain.
Qualifier Romina Oprandi, who beat world No. 2 Kim Clijsters in the second round, moved into the semis with a 7-6 (7-3), 6-4 decision over Kimiko Date-Krumm. Oprandi had six service breaks.
Unseeded Jelena Dokic will go against Oprandi in the semifinals. Dokic got by Johanna Larsson 7-6 (7-2), 6-4 by winning 69 percent of the points on serve.