Current World Cup leader Fischnaller dominated the men's event at Bokwang Phoenix Park in Pyeongchang, the venue for the sport at the 2018 Winter Olympic Games.
The 39-year-old Italian finished the qualification phase fastest and took victory in the final after his opponent in that contest, Russian Dmitry Loginov, failed to finish.
The men's small final was won by Russia's Andrey Sobolev, who beat Austria's Alexander Payer by 0.19 seconds to take third place.
Meanwhile, in the women's competition, the overall parallel World Cup leader heading into Pyeongchang, Germany's Ramona Theresia Hofmeister, topped the standings after the qualification phase of competition ahead of Zogg and Natalia Soboleva of Russia.
Hofmeister was beaten in the semi-finals and Zogg edged out Italian Nadya Ochner in the final, the Swiss snowboarder triumphing by 0.03 seconds.