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.
Millions of Getty images now available for free via embed tool
Ray Liotta sues skin care company over use of likeness