The 18-year-old Shiffrin, who was down by seven points in the slalom standings heading into Saturday's race, turned in the fastest time in the second run of the day and finished with a winning two-run time of 1 minute, 55.60 seconds.
It was Shiffrin's fourth slalom victory of the World Cup season and made her the first U.S. champion in the discipline since Tamara McKinney in 1984.
Bernadette Schild of Austria took second in 1:55.80, followed by Tina Maze of Slovenia, who had led the slalom standings before the race.
"Straight after the first run, I went to the athletes' tent and tried to figure out what I needed to do to make it better," said Shiffrin, who trailed after the first run by a wide 1.17 seconds. "I asked everybody around me. They all said the same thing: you have to let it go, you cannot hold back because there is nothing to lose."
Shiffrin called Maze, who had already clinched the overall World Cup points race but was less aggressive in her second run, an inspiration.