The 19-year-old Gulini of Salt Lake City claimed the U.S. national title as the top American finisher at Park City's Canyons Resort.
Austria's Maria Ramberger took third overall for the women, while Bulgaria's Alexandra Jekova was fourth.
Meanwhile, Austria's Markus Schairer and teammate Alessandro Haemmerle finished 1-2 in the men's final.
Nate Holland, who got tangled up with young Australian Jarryd Hughes in the finals, finished fourth but still claimed the U.S. national championship as the top American man.