The third-seeded Cibulkova went a set down before staging a comeback and pulling out a 3-6, 6-4, 6-4 victory that is her first title since winning the Carlsbad event last year.
The triumph provided a measure of revenge for the Slovakian, who fell to Radwanska in January in the final of the Apira International at Sydney. She improved to 1-5 all-time against the Polish world No. 4.
Radwanska, however, didn't give in easily, turning back four match points before finally succumbing.
She came up short in her bid to secure a third 2013 title.