Rybarikova managed five service breaks in eight games in beating Bartoli 6-4, 6-1. Bartoli had won four of the five times previously she'd played Rybarikova.
Both players landed just 48 percent of their first serves but Rybarikova was able to make that into more of an advantage as she won 54 percent of the points on Bartoli's serve.
Second-seeded Alexandra Dulgheru was ahead 6-1, 5-0, with six breaks of serve to her credit, when Zuzana Kucova retired with a hamstring injury. Roberta Vinci, at No. 6 the only other seeded player on Monday's schedule, advanced with a 6-2, 6-3 decision over Silvia Soler Espinosa.
Maria Elena Camerin, inserted into the draw when eighth-seeded Lourdes Dominguez Lino withdrew because of a foot injury, claimed a 6-4, 7-5 win over Evgeniya Rodina.
Also Monday, Yaroslava Shvedova beat Chang Kai-chen 6-3, 2-6, 6-2; Jill Craybas topped Akgul Amanmuradova; and qualifier Estrella Cabeza Candela defeated Arantxa Parra Santonja 6-3, 7-5.