Cornet needed a second-set tiebreaker to best her Ukrainian opponent 6-2, 7-6 (8-6) on the red clay court at Bogota.
Argentine Paula Ormaechea posted an opening-day win as well, dispatching Russian Nina Bratchikova 7-5, 6-2, while Luxembourg's Mandy Minella also advanced with a 6-4, 6-3 decision over German Tatjana Malek.
Former world No. 1 Jelena Jankovic is the top seed in this year's Bogota event.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys