Bartoli, a former Wimbledon runner-up, struggled again, losing to Zakopalova 4-6, 6-1, 6-2 in the opening round on the red clay courts of Warszawianka Tennis Centre.
No. 3 seed Li Na of China, meanwhile, emerged with a triumph in her first-round match against Romanian Ioana Raluca Olaru 7-6 (7-4), 6-0.
Elsewhere, fifth-seeded Chinese Zheng Jie hung on to defeat Belarus' Olga Govortsova 6-1, 5-7, 7-5 and Magdalena Rybarikova bounced eighth-seeded American Melanie Oudin 6-0, 6-2.
The second round of the Warsaw Open gets under way Wednesday, and will feature matches involving top seeds Caroline Wozniacki and Elena Dementieva. Wozniacki is scheduled to face Slovenian Polona Hercog while Dementieva will meet Bulgarian qualifier Tsvetana Pironkova.
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