Schild, who now has a career tally of 31 victories in the discipline, had two flawless runs to finish in an aggregate one minute 51.42 seconds and beat second-place Tina Maze of Slovenia by 0.79 seconds.
Shiffrin started her eighth World Cup event as No. 40, ended the opening run in 12th position before posting the fastest time in the final run. She finished 1.30 behind Schild, who lost 0.24 to Shiffrin in the final run.
Shiffrin, who became the youngest American national slalom champion last spring, impressed with an all-attacking yet error-free second run, in which she made many turns extremely close to the gates.
"I have been working so hard for this moment," said Shiffrin, who finished eighth in the Aspen slalom last month. "Schild, Zettel, Hosp, Vonn; I have been watching all these top girls for the past 10 years. And now I am here myself, it really feels crazy."
While Shiffrin stepped onto the podium for the first time, the 30-year-old Schild equalled Vreni Schneider's record with her 47th World Cup slalom podium.
Marie-Michele Gagnon of Lac-Etchmenin, Que., was the top Canadian in 14th place.
“I was quite disappointed with my first run. I skied well but I just didn’t have that fire I needed to get in the top 10,” said Gagnon, who was 18th after the first run. “I’m happy because the second run was better.”
Erin Mielzynski of Guelph, Ont., was 22nd. Madison Irwin of Toronto and Elli Terwiel of Heffley Creek, B.C., did not qualify.
Shiffrin said she was impressed by meeting Schild, one of her idols.
"It's the first time I've been talking to Marlies in person," Shiffrin said. "I couldn't believe she was congratulating me after the race. What a moment!"
Schild was just as excited by the teenager's performance.
"Of course I saw her in Aspen, she's a real talent," Schild said. "I see a lot of myself in the way she is skiing. She has what it takes to become a great champion in the near future."
Shiffrin's American teammate Lindsey Vonn finished 18th and retained the lead in the overall standings. The three-time champion has 612 points, followed by Schild with 440 and Austria's Anna Fenninger, who usually skips slalom, with 368.
Defending overall champion Maria Hoefl-Riesch of Germany made costly mistakes in the final part of both runs and finished ninth, 1.99 behind Schild. In the overall standings, Hoefl-Riesch is fifth with 326 points.
After a solid first run, Vonn lost speed and time going into the final section of her second run, finishing 3.01 off the lead.
Vonn hasn't been on a slalom podium for more than two years.
"It's getting closer (to the podium)," she said. "I am hoping to get back in the (starting) top 15 and that will help a lot."
Vonn said she has gained confidence in the technical events again this season, helped by her victory in the giant slalom in Soelden, Austria, in October.
"I know I have the speed, it's a matter of putting two runs together," she said. "I just feel comfortable in any race right now. Every time I am in the starting gate, I am going to try to win. I am just having fun."
Vonn's American teammate Julia Mancuso skied out just a few seconds after the start of her first run when her right ski hit a gate and she lost balance.
After a short break, the women's World Cup will continue Tuesday with another slalom event in Zagreb, Croatia.