Hansdotter turned in a combined two-run time of 1 minute, 50.17 seconds to edge the Schild sisters of Austria, who took second and third places, in the final pre-Olympic Alpine event.
Hansdotter had made the podium eight times before Sunday's, all of which were second-place finishes.
"It was a tough day," Hansdotter said. "Conditions were really soft in the first run, but a bit less so in the second. I did my best and it feels really good to have my first victory."
Hansdotter edged Mariles Schild by a razor-thin 0.05 seconds and Bernadette Schild by 0.15 seconds.
Mikeala Shiffrin of the United States led after the first run, but a mistake early in her second trip down the hill cost her and she wound up in seventh place with a time of 1:50.89.
World Cup overall leader Maria-Hoefl-Riesch of Germany also struggled in the second round and finished 23rd.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys