Gut, 21, finished 0.38 seconds behind Maze, 29, who leads the overall World Cup standings.
The Ticino native finished ahead of American Julie Mancuso, super-G gold medal winner in the 2006 Winter Olympics, for the eighth podium finish since her World Cup debut as a 16-year-old in December 2007.
But the results of the race, dogged by fog and visibility problems, were overshadowed by Vonn’s crash, which knocked her out of competition for the rest of the season.
The 28-year-old US star broke her leg and tore two ligaments in her right knee after falling on her second run about half-way down the Streicher course.
She was airlifted to a hospital for treatment.
“It was a really bad crash,” former Swiss ski champion Didier Cuche told Eurosport.
“She was pushing very hard,” Cuche said.
“She jumped a long way and missed the landing.”
The second-place result for Gut marks her first finish in the top three since she won the downhill at Val d’Isère, France on December 14.
It also marks her first podium finish for a super-G race since she came third at Cortina d’Ampezzo, Italy in January 2011.