Pauline Parmentier had little trouble in dispatching Cibulkova 6-2, 6-2 and moving into the second round.
Top-seeded Victoria Azarenka also posted a first-round win Wednesday, beating Su-Wei Hsieh 6-3, 6-4. The final first-round match saw Anastasiya Yakimova defeat eighth-seeded Anastassia Rodionova 6-3, 6-0.
In second-round play, fourth-seeded Elena Vesnina beat Tatiana Poutchek 7-5, 6-4; No. 5-seeded Ioana Raluca Olaru swept Mariya Koryttseva 6-2, 6-2; local-favorite Akgul Amanmuradova upset seventh-seeded Olga Poutchkova 6-3, 6-4; and Ksenia Palkina beat Vlada Ekshibarova 7-5, 5-7, 7-5.
The tournament wraps up Sunday with the Tashkent Open champion taking home $21,165.
Swim Week Miami Beach 2014 [PHOTOS]