Zettel finished in a combined time of 1 minute, 42.46 seconds to edge Schild by 0.67 seconds. Tina Maze of Slovenia was third in a race that part-time Park City resident Lindsey Vonn skipped as she recovers from an intestinal illness.
Schild was seeking her 34th career slalom win, which would match the discipline record of Swiss great Vreni Schneider.
Teenager Mikaela Shiffrin of the U.S. was in the lead for a few skiers before winding up seventh. Still, it was another solid showing for the 17-year-old who's from down the road in Vail.
Aksel Lund Svindal of Norway won the men's super-G, completing a weekend sweep at Lake Louise, Alberta. Svindal also won Saturday's downhill, making him the first man to win both events at Lake Louise since Bode Miller in 2004.
Svindal was timed in 1 minute, 34.96 seconds, beating runner-up Adrien Theaux of France by 0.85 seconds. Joachim Puchner of Austria was third in 1:35.86, and Ted Ligety of Park City was fourth in 1:35.87.
In Igls, Austria, Olympic luge champion Felix Loch led a German sweep of the top five positions at the season-opening race. Loch set a track record in his first run and was fastest in the second to finish in an aggregate time of 1 minute, 40.229 seconds for his 11th career win.
David Moeller was 0.307 back in second, and Johannes Ludwig took third.
In Kolomna, Russia, Koen Verweij earned his first career World Cup individual victory by winning the men's 1,500-meter race.
Verweij finished in 1 minute, 45.56 seconds, edging Bart Swings of Belgium by 0.21 seconds. Brian Hansen of the United States was another 0.14 seconds behind for third.
Former Olympic champion Claudia Pechstein of Germany won the women's 3,000 meters.