Shiffrin, the most successful skier in World Cup history and hoping to end the season with a sixth overall Crystal Globe, finished 23rd but the eight points stretched her lead over German Aicher to 125 with six races remaining across all disciplines.
The American does not race in downhill and has focused on technical disciplines this season, apart from entering one super-G in December - her first in two years - ahead of last month's Milano Cortina Olympics. A win is worth 100 points.
The World Cup super-G title battle will go down to the wire at the finals in Norway on March 22nd, with Italy's Sofia Goggia leading Alice Robinson of New Zealand by 63 points.
Goggia finished ninth while Robinson, now the only other woman who can win the super-G title, was joint fourth with France's Romane Miradoli.
"I feel confident. We've got one more race so I'm happy to give that everything, but it's a little bit frustrating," said Robinson, who will have to finish at least second in the final race to have any chance of the title.
Goggia said she had been struggling with her skis: "I had no control over them at all. Luckily, I could contain a little bit the damage in the upper part (of the piste)."
Norway's Kajsa Vickhoff Lie was second, 0.26 slower than Curtoni's one minute 29.07 seconds, with Italy's Asja Zenere springing a surprise by racing to third and her first World Cup podium after starting 33rd.
Aicher skied out, leaving her 145 points behind Goggia and out of super-G title contention.
Curtoni's fourth career win, and the 35-year-old's first on the World Cup circuit since 2022, completed a triumphant weekend for Italian skiers on home snow after Laura Pirovano's downhill double on Friday and Saturday.
Italian great Alberto Tomba was on hand to present Curtoni with her winner's trophy.
"I knew I still had it. But when the victory and the podium don't come, then you start to ask yourself questions," said Curtoni. "Today I was able to find that confidence... it's very nice to be there at the front even now after so many years".
