American Vonn has been forced to end her season after injuring her knee but is still 28 points ahead of Gut.
Compatriot Shiffrin, who turns 21 next week, beat Switzerland's Wendy Holdener by a hefty 2.36 second margin over the two runs with home favourite Veronika Velez Zuzulova third.
Shiffrin has now won four slaloms this season, two of them since she came back from a right knee injury sustained in December. She now has 19 career World Cup victories to her credit.
Hansdotter finished 10th on Sunday but that was enough to secure the crystal globe. She leads Zuzulova by 105 points with 100 still to be won at the World Cup finals in St Moritz, Switzerland.
The title was the Swede's first in the discipline.
"Frida has been just as consistent as I have been, or even more consistent in the past three, four years," said Shiffrin, who missed five races due to her injury.
"She has walked away with however many second places, but you have to be really consistent just to get on the podium. But she deserves to win the globe."
(Writing by Alan Baldwin in London, editing by Toby Davis)
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