Fourteen years separated the two finalists but there was little between 16-year-old Vekic and the 60th-ranked Hantuchova.
The Slovak struck first in the opening set, breaking her opponent's serve to lead 4-3 but Vekic hit back immediately to level the score.
Hantuchova dominated the tiebreaker, however, and despite throwing away a 5-2 lead regained control to win 7-5.
The second set was just as tight as the first but a break of serve at 5-4 proved decisive for Hantuchova, who sealed a straight sets win.