Schild turned in a combined time of 1 minute, 34.95 seconds, 78/100ths of a second ahead of Finland's Poutianen and nearly 2 seconds ahead of third-place Tina Maze of Slovenia.
"It's really difficult to compete against Marlies at the moment," Poutianen said afterward. "Her form is nothing short of superhuman."
Poutianen led the competition after the first run.
Julie Mancuso was the top American finisher in 21st place. Lindsey Vonn of the United States and Germany's Maria Reisch were among the 33 racers who ran into trouble on the tricky course and failed to finish.