In the second heat, Austria's Anna Gasser conquered her nerves to post a sizzling score of 95.50 on Thursday and qualify for the women's snowboarding slopestyle Olympic final.
26-year-old Zurich native Derungs secured top spot when she scored 87.50 on her second run to push Australian Torah Bright into second place.
Also qualifying directly for Sunday's final were Canada's Spencer O'Brien and Enni Rukajarvi from Finland, while Britain's Jenny Jones - a former X Games champion - missed out in agonising fashion as she came fifth.
Jones is not out of the competition, however, as she will run in the semi-finals on Sunday, as will 10th-placed compatriot Aimee Fuller.
In the second heat, American Jamie Andersson had a scintillating run of her own but had to be content with second place with a score of 93.50, while Elena Koenz from Switzerland and American Karly Shorr also qualified automatically for Sunday's final.
"I'm so relieved, it's like a big stone fell from my heart," said second heat winner Gasser at the Rosa Khutor Extreme Park.
"I was so nervous, I've never been that nervous in my life before. I'm straight to the finals, that's the best thing I could wish for," she added with a beaming smile.
"I won't be as nervous in the final, I'm already top 12 and that's a good result for me."
Another U.S. athlete, Ty Walker, rode down the side of the course and skipped her second run entirely due to injury.
"I have a bone bruise in my heel, I got it on the second day of practice, and each impact makes it a little worse," she told Reuters as she watched her team mates on their final runs.
"I figured that seeing as everyone makes it through to the semis on Sunday, I'd rather just preserve myself and give it my all for one day."
The top four from each heat went directly into Sunday's final, with the rest of the competitors going to a semi-final earlier that day to decide the remaining four places.
The opening ceremony for the Sochi Games, Russia's first winter Olympics, takes place on Friday.