Next up for the diminutive hard-charging Slovak will be eighth-seeded Zhang Shuai of China, who got by Ajla Tomlianovic of Croatia 6-1, 5-7, 6-2.
Erakovic matched Cibulkova in most of the match stats, but committed nine double faults.
Also advancing Thursday were Caroline Garcia of France and Christine McHale of the United States.
Garcia eliminated second-seeded Eugenie Bouchard of Canada 3-6, 6-4, 6-1. McHale also needed three sets to get past third-seeded Kaja Kanepi of Estonia 6-1, 2-6, 6-4.
Celebrity Couples of 2014 [PHOTOS]