Aicher clocked the fastest run in one minute 14.04 seconds in foggy conditions, with Vonn pushing hard to finish 0.27 seconds behind in second place and seal a seventh podium in eight races.
Czech Ester Ledecka was third in the Italian resort for her first podium of the season.
"I'm pretty happy with how I skied today. The win is a bonus, I guess. It was a good run from top to bottom, and I'm happy that I could do it," said Aicher, who finished fifth in Saturday's downhill.
"Yesterday was pretty okay as well. The skiing was good, and a few mistakes. I'm happy that I could just push through and have no mistakes for once."
Vonn is in astonishing form as she prepares for an Olympic comeback at the age of 41.
She retired from the sport in 2019 and had a partial knee replacement in April 2024, but returned to competition later that year and has been enjoying a fairy-tale comeback that has defied age and expectation.