Suter - winning her fourth World Cup race but first in almost three years - came home ahead of Slovenian slalom specialist Tina Maze with Austrian Anna Fenninger filling third spot.
Vonn, the overall World Cup leader and winner of the previous two super-G races, finished 18th - over half a second off the pace and putting an end to her run of 19 successive podium finishes in the discipline - in what was her worst result since December 2008.
The American has been suffering from a stomach virus this week and came in fourth in the downhill on Saturday.
"I know that I have not been myself these past few days," she said.
"I feel really flat, I am unable to do anything on the turns, I am just passive."
Suter, 27, managed to prevail despite a big mistake on the lower part of the course but still had 34 hundreths of a second to spare over Maze, Olympic silver medalist in the discipline but who has won World Cup races in every other category bar this one.
"I am very happy with my two days here," said Suter, who was third in the downhill.
"To be first today (Sunday), it is great to be the fastest for once."