Revived by this year's Sochi Olympics, where she won a silver and a bronze after years fighting injury, the 2007 overall World Cup winner won in a combined time of one minute and 44.90 seconds.
The 31-year-old beat Sweden’s Frida Hansdotter by 0.19 seconds and compatriot Kathrin Zettel, who seized the overall World Cup lead, by 0.95. Since making her return from two knee injuries in 2009, the Austrian all-rounder has shone more in speed events and took her Sochi medals in the combined and Super-G.
Her last World Cup win before Sunday was in a slalom in Maribor, Slovenia, in January 2008.
"The last time I won a slalom was in 2008. It’s like another lifetime," she said. "To win today is a bit like scoring my first victory. It means a lot when you’ve gone through all these troubled years.
"I cannot say I’d stopped believing in my chances because I felt in training I was not finished. I thought a top five was possible, maybe a podium. But in slalom, with all these young girls coming up, I didn’t think I still had my place."
The young generation, personified by Shiffrin, were not in their best shape on the Aspen course.
The 19-year-old American clocked the fastest morning time but faltered in the afternoon, perhaps weakened by a stomach bug that had been bothering her all week.
"It’s hard when you ski great in training and then in the race nothing goes according to plan," said Shiffrin, who finished 5th, 1:08 behind Hosp.
Despite the disappointment, it was an improvement from 11th in her previous race in the Finnish resort of Levi this month.
"After Levi I lost a bit of confidence," she said. "I knew I needed to do something special in the second run today but that little extra something wasn’t there."
The women’s circuit moves to Lake Louise next weekend for a downhill and a Super-G.
(Reporting by Manuele Lang, editing by Alan Baldwin)
