Schild turned in a two-run time of 1 minute, 43.85 seconds, 34/100ths of a second faster than teammate Kathrin Zettel.
Tina Maze placed third with a 1:45.01 and Sara Schleper of the United States took 11th.
Vonn came in tied for 16th, but it was enough to move to within 23 points of Germany's Maria Riesch in the overall World Cup standings. Riesch failed to finish the second run Saturday.
"I was hoping to stay as close to Maria as possible, but to make up as many points as I did this weekend was definitely above my expectations," Vonn said.
The final four races of the women's season take place in Lenzerheide, Switzerland next weekend.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys