Shiffrin, 17, turned in a combined time of 1 minute, 39.85 seconds and edged Austria's Michaela Kirchgasser by 0.22 seconds to become the third-youngest ladies' slalom world champ in history.
"In the first run, I wasn't quite awake and aware of the situation," said Shiffrin, who is ranked sixth in the overall World Cup women's standings. "Two minutes before the second run, I felt I could win and I did."
It was the third slalom victory for Shiffrin in her second World Cup season.
Shiffrin turned in a solid 50.59 in her opening run and then finished the second run in 49.26. Kirchgasser was actually faster in her second run that Shiffrin but was 0.10 seconds slower than the young American in the first trip.
Frida Hansdotter of Sweden took third place with a 1:40.11. Overall points leader Tina Maze of Slovenia placed fifth and Maria Hoefl-Riesch of Germany, who is second in the overalls, hooked a gate and did not finish.