The 28-year-old watched as Briton Hunt accidentally added an extra twist to his final dive, giving him a zero for the effort and opening the door for Parades.
The Mexico City native nailed his fourth and final dive to raise his World Series total to 720 points and take home the 2017 King Kahekili trophy.
Hunt ended the 2017 season with 710 points while fellow Briton Blake Aldridge finished third overall with 580.
On the women's side Australian Rhiannan Iffland defended her crown to win her second title at the iconic waterfall setting in Lago Ranco.
Iffland overcame injury to finish the season with 890 points overall, 150 points ahead of her countrywoman and second place finisher Helena Merten. Mexican Adriana Jimenez finished third with 690 points.
The Red Bull Cliff Diving World Series began in 2009 and takes place across six locations worldwide. It sees competitors attempt multiple twists and somersaults mid-air from heights as great as 90 feet (27 meters).
(Reporting by Rory Carroll; Editing by Peter Rutherford)
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