In a match between two women playing their first tour final, the 20-year-old Quevedo, ranked 90th in the world, started slowly.
After the final was pushed back to Monday due to heavy rain earlier in the hard-court tournament, Podoroska, a 29-year-old ranked 200th in the world, broke her American-born opponent twice to lead 3-0 in the first set.
Quevedo, who made her tour debut in Auckland in January, broke back in the fourth game but Podoroska stayed in control to take the set.
The players exchanged breaks at the start of the second set before Quevedo broke in the 10th game.
That swung momentum her way as she won the first five games of the third set; Podoroska briefly fought back before Quevedo clinched victory on her second championship point.