Burel, 20, a former world number one in the junior rankings who is coached by French former tennis star Thierry Champion, was playing in her first final on the WTA tour.
The 25-year-old is the first Czech to lift the Suzanne Lenglen Cup since Hana Mandlikova, who represented Czechoslovakia, triumphed in 1981.
Krejcikova won six games in a row to take the opening set after dropping serve in the first, before Pavlyuchenkova gained the upper hand in the second set.