Schild was fastest in both runs and finished in an aggregate time of two minutes 1.32 seconds to beat second-place Tina Maze of Slovenia by 1.40 seconds.
Austria's Michaela Kirchgasser was 2.27 seconds off the lead for her first career podium appearance in slalom.
Lindsey Vonn of the United States finished ninth to remain in the overall lead, while defending overall champion Maria Hoefl-Riesch of Germany caught a bump and skied out early in her second run.
Anna Goodman of Pointe Claire, Que., was 23rd. She was the only Canadian to qualify for the second run.