Schild was in sixth place after the first run and came away with the win in a combined time of 1 minute, 55.63 seconds.
"The upper part [of the course] didn't work out the way I wanted but I pushed in the lower section and it paid off," said Schild, who broke the record of 34 World Cup slalom wins she had held with Switzerland's Vreni Schneider.
Mikaela Schiffrin of the United States, the leader after the first run, wound up in second place, 0.41 seconds behind Schild.
"Having Marlies next to me on the podium is great," said Schiffrin, who finished third in Saturday's giant slalom. "I always want to win but she skied better and was faster. She is still one of my idols and she keeps inspiring me."
Maria Hoefl-Riesch of Germany came in third and took over first place in the overall women's standings.