Rain in Tokyo forced the postponement of all but the five matches scheduled for the enclosed center court.
Among those contests, the 12th-seeded Cibulkova posted a 6-3, 7-6 (7-3) victory over Spain's Anabel Medina Garrigues and No. 14 Vinci outlasted Czech Barbora Zahlavova Strycova 6-4, 4-6, 7-5.
Also Sunday, Serbia's Jelena Jankovic bested Yanina Wickmayer of Belgium 6-3, 6-3.
The rainy conditions necessitated some 19 matches to be scheduled for Monday.
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