New Zealand freeski team-mate Sam Smoothy, also of Wanaka, shared third place with Lucas Swieykowski (Argentina).
McDougall only made the event as a wild-card entrant but surprised everyone with what the judges said was the most fluid run on an extremely technically difficult Mt Corvatsch.
"I was stoked to be up on the podium," McDougall said. "The competition was incredibly well run and it was a boost to have my team-mates on the podium with me."
Up against 43 riders from 10 countries, McDougall, a member of the New Zealand freeski development squad in his first year out of Mt Aspiring College, felt the pressure to perform.
"It was pretty scary being invited to my first overseas competition. Arriving in to St Moritz on the train I could see the Corvatsch face and it looked pretty comparable to the Treble Cone Chutes, my home field, and it was packed with snow."
In the women's field, New Zealand freeski No 1 Kuzma continued her run of good form by skiing to victory.
Kuzma earlier won at the Canadian Open, and made the podium in her first world tour qualifying event last week.
Kuzma's twin sister, Maria, was third in the snowboard division in St Moritz.
