Cibulkova downed the Frenchwoman 6-1, 7-5 in a 95-minute match at Carlsbad, Calif., picking up her second career title in four finals appearances.
Her only other championship came when she bested Kaia Kanepi in Moscow last year.
Bartoli, meanwhile, fell short in a bid for her first victory since last year's event in Osaka.
Notable deaths of 2014 [PHOTOS]
UPI horse racing weekend preview