Hansdotter, who placed third in Maribor at the weekend, clocked a total run time of 1:51.40 in Flachau, with Norway's Nina Loeseth placing second, 0.58 seconds back.
The bronze medal was shared between Olympic champion Mikaela Shiffrin and Wendy Holdener, who both crossed the line 0.78 seconds back.
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Swede Hansdotter lost almost four tenths of her first-run lead in the second, but held onto to win the last race of the World Cup series ahead of next month's World Championships.
Frida Hansdotter takes fine win in Flachau
"I didn't know it was that fast, but for sure I felt I had a good run," she said.
"But I got a little scared when in the banana [delay gate] because I hooked a little bit on the skis.
"I didn't get that speed over the last roller, but it was really good, so I'm satisfied."
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