In a match that featured 11 breaks of serve, Bartoli reached the third round by ousting Vera Dushevina 6-2, 6-7 (3-7), 6-4. Bartoli will next meet Polona Hercog, who got past Varvara Lepchenko 6-3, 6-2.
Rodionova advanced on Tuesday, as did Serena Williams and second-seeded Samantha Stosur.
In other second-round matches, Sabine Lisicki defeated Andrea Hlavackova 2-6, 6-3, 6-4; Lucie Safarova eliminated Mirjana Lucic 6-2, 6-0; and qualifier Yaroslava Shvedova ousted Yanina Wickmayer 6-2, 7-6 (7-2).
Marina Erakovic earned a third-round meeting with Serena Williams by defeating Anna Tatishvili 7-5, 6-3.