Gut finished with a combined two-run time of 2 minutes, 25.16 seconds, nearly a full second ahead of Austrian Katherine Zettel.
Viktoria Rebenseberg of Germany took third with a time of 2:26.44. Mikaela Shiffrin was the first U.S. finisher with a sixth-place time of 2:26.78.
Gut was the top finisher in Saturday's first run and followed up with a solid second run that nailed down her first career win in the giant slalom. "In the second run I just thought about skiing fast and didn't think about what could happen. It is really nice that I am finally back on what I can do in GS," she said.