Kvitova, a former Wimbledon champion, eliminated Croat Petra Martic 6-3, 6-2 in 69 minutes and will face Romanian qualifier Alexandra Cadantu Saturday.
Vinci needed just 67 minutes to get past Czech wild card Karolina Pliskova 6-1, 6-0 and advance to a semifinal match against German Annika Beck Saturday.
Cadantu reached the semifinals with a 5-7, 6-3, 6-3 comeback win over Israeli lucky loser Shahar Peer.
Beck advanced with a 7-6 (7-1), 6-0 victory over Italian qualifier Maria Elena Camerin.
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