With Austrian world champion Marlies Schild injured and overall World Cup holder Lindsey Vonn of the United States taking a break until the New Year, the 17-year-old won with a combined time of one minute and 45.36 seconds.
Sweden's Frida Hansdotter, the first run pacesetter, was second and 0.29 seconds adrift while Slovenia's World Cup leader Tina Maze was third, 0.52 off the pace.
"My heart just stopped and it will take me a year to realise what I've just done. I was just trying to fly," said former junior world bronze medallist Shiffrin, who had only twice before stood on the World Cup podium.
Shiffrin, who was third in a slalom in Levi, Finland, last month and also third in the Austrian resort of Lienz a year ago, delivered a perfect second leg to fend off the challenge of her more experienced rivals in the last race before Christmas.
"Now I'm probably going to hug my mum a lot. My Dad will also be coming over for Christmas. I'll try to calm down and prepare for Semmering," added the skier from Burke Mountain Academy in Vermont.
The women have two more races in the Austrian resort next week before the end of the year.
While she is not the youngest skier to win a World Cup race - several women having done so at 16 - Shiffrin is the second youngest American to do so after Judy Nagel in 1969 and certainly one of the big talents to emerge in recent years.
Maze's third place left her leading the World Cup overall standings with 919 points, 387 more than nearest rival Maria Hoefl-Riesch of Germany.
"It was the last race before Christmas and I really meant to finish on a high note. But now is more than time for me to rest," said the Slovenian.
Schild flew back to Austria for checks after falling in morning practice.
"On one of the bumps, I lost control and I landed on my back. I was blocked by a ski. For the time being I feel pain in the back and in the right knee," she said on the Austrian Ski Team website.
It was a bad day generally for the Austrians as Kathrin Zettel, winner of the previous World Cup slalom in Aspen, failed to complete the first run while the best placed member of the team was Michaela Kirchgasser, who was suffering from flu and finished ninth.