Slovakia's Cibulkova worked hard in her 6-1, 6-7 (5-7), 7-6 (7-3) victory over Spaniard Lourdes Dominguez Lino, barely sneaking into the second round at Autotron Rosmalen.
In a pair of upsets Monday, sixth-seeded Mona Barthel of Germany fell to Spanish qualifier Garbine Muguruza 7-5, 1-6, 6-2 and No. 8 seed Kristina Mladenovic of France bowed to Bulgarian Tsvetana Pironkova 6-4, 6-4.
Other first-round winners Monday included American Lauren Davis and Romania's Simona Halep, who was coming off a victory in last week's event in Nuremberg.
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