Suter, who took third in Saturday's downhill, started after all pre-race favourites were already down but was fastest at all intermediate times and finished in 1 minute, 9.55 seconds to earn her fourth career World Cup victory.
Tina Maze of Slovenia came 0.34 behind in second, and Anna Fenninger of Austria took third, another 0.40 behind.
"To be the fastest of all for one day, that's just great," Suter said. "In the downhill, I took too many risks so I tried to do better today. But at super-G, you have only one chance after course inspection so I am very happy how things worked out."
Suter led a strong showing by the Swiss team, with Fraenzi Aufenblatten and Lara Gut coming fourth and fifth respectively.
Vonn was the first starter from the top group, but lacked the strength to be competitive after struggling with a stomach illness over the last week.
"I didn't really have the self-confidence and I didn't have the power that I normally have," Vonn said. "I am still not myself. ... I just feel flat."
Vonn, who won both previous super-G races this season, lost the ideal race line several times and struggled to correct herself. She finished 1.53 seconds off the lead.
It was the first time the American missed a World Cup super-G podium since placing eighth in Cortina d'Ampezzo, Italy, in January 2009, and it was Vonn's worst super-G result since not finishing in St. Moritz, Switzerland, a month before that.
"You can't be fast always. Maybe it would have been smarter if I had not done these races," said Vonn, who placed fourth in Saturday's downhill. "I definitely struggled this weekend but I am not going to put too much weight into it."
Vonn remained in the lead of both the overall and the super-G standings. She has 704 points for the overall championship, followed by Austria's Marlies Schild with 540 and Maze with 483.
Defending overall champion Maria Hoefl-Riesch of Germany, who missed both races this weekend due to illness, has 326 points, which leaves Maze as Vonn's main challenger for the overall title.
"I always try to win every race," Maze said. "Today, I saw all the great names coming down and not beating my time, so I knew it was a good run. I didn't fully attack in the middle part, that's where I lost the race to Fabienne."
Vonn's American teammate Julia Mancuso came 1.01 behind in eighth to earn her second top-10 finish of the weekend.
"That's always good," Mancuso said. "I think my skiing is better than that but from third place on it's really close."
Mancuso said she had problems in adapting to the changed course conditions as warmer weather had made for softer snow than the day before.
"I think I gave the course too much respect," she said. "The snow is a lot softer ... The bumps were not knocking out anyone. It's just sometimes hard when you're expecting a plan to change your plan halfway through your run. I guess I just overskied."
The women's World Cup travels to Cortina d'Ampezzo for a downhill and a super-G next weekend.