Vinci was broken four times in the second set by Hercog.
The Italian will face fifth-seeded Spaniard Lourdes Dominguez Lino, who beat Nastassja Burnett of Italy 7-5, 4-6, 6-3.
Third-seeded Kristina Mladenovic was eliminated after a second-round upset by Estrella Cabeza Candela of Spain. The 20-year-old Frenchwoman lost 6-3, 2-6, 7-6 (6). Candela faces Renata Voracova in the quarterfinals.
Fourth-seeded Klara Zakopalova of the Czech Republic was safely through after beating Karin Knapp of Italy 6-3, 4-6, 6-4 in a match which lasted 2 hours, 40 minutes.
Zakopalova will play Dinah Pfizenmaier of Germany.