Gagnon was 16th after the super-G run in the morning but turned in the fastest time of the day in the slalom run to make it to the top of the podium.
"I knew I had to do a really good slalom since I was more than a second behind after the super-G run," said Gagnon. "So I entered the slalom without too much of expectation. I skied freely and that helped me give my best."
Gagnon won her first World Cup victory of the season with a 51.05-second slalom that gave her a combined-run time of 2 minutes, 05.55 seconds.
Michaela Kirchgasser was in second place. 0.32 seconds behind the Canadian. Germany's Maria Hoefl-Riesch took third.
It was a good day for the Austrians, who placed five skiers in the top 11.
Laurenne Ross was the only American to finish the race, taking 20th with a 2:08.70.