The 13th-seeded Jankovic, who won the Cincinnati title in 2009, was ousted by China's Peng Shuai in a marathon 5-7, 7-5, 7-6 (10-8) battle.
Jankovic failed to convert on numerous match points in a bout delayed by rain in the final set.
Meanwhile, ex-French Open titlist Schiavone, seeded 14th, fell to wild card and fellow Italian Camila Giorgi 6-1, 6-3 at the Lindner Family Tennis Center.
Also Monday, 11th-seeded Slovakian Dominika Cibulkova advanced with a 6-4, 6-4 decision over Uzbekistan qualifier Akgul Amanmuradova.
Germany's Mona Barthel and Polish qualifier Urszula Radwanska also advanced with victories.
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