After finishing 14th in the downhill at Garmisch-Partenkirchen a day earlier, Gut powered to victory in the Super-G while US ski queen Lindsey Vonn had to settle for third on Sunday.
Vonn had picked up the 76th win of her career in winning Saturday's downhill with a commanding display down the Kandahar to finish a second and a half ahead of her nearest rival.
But 24 hours later she had to make do with a podium place, 0.23 seconds behind Gut's winning time of one minute 20.51 seconds, while Germany's Viktoria Rebensburg was second at 0.15 seconds back.
It was the 124th time Vonn has finished on the podium of a World Cup race.
The result keeps the American on top of the overall leaderboard with 1,060 points, while Gut is second on 973 and Rebensburg third on 820.
Meanwhile, in South Korea, Switzerland's Janka took the Alpine Ski World Cup men's super-G race at Jeongseon Alpine Centre on Sunday, his first career victory in the discipline.
The 2010 Olympic giant slalom champion posted a time of one minute, 26.16 seconds at the South Korean venue, which is hosting the World Cup as a test event for the 2018 Winter Games.
Christof Innerhofer of Italy finished second on 1:26.98, followed by Vincent Kriechmayr of Austria on 1:27.22.
Janka has achieved just one other podium finish in the current World Cup season, and none of his ten previous World Cup wins had come in super-G (super giant slalom).
"I took some risks, and everything worked out," Janka said.
"The slope was really good," he said.
"Some jumps were a little bit difficult and in super-G you never know what's going to happen."
Seventh among 54 skiers to start, Janka posted his time and watched one contender after another fall by the wayside.
Andrew Weibrecht of the United States, Kjetil Jansrud of Norway and Dominik Paris of Italy — ranked second, third and fourth on the World Cup super-G standings — all failed to finish their races.
Janka swept up three World Cup victories at Beaver Creek in Colorado in December 2009, and said he enjoyed Jeongseon's "cold, nice" snow, which he felt was similar to surfaces he had seen in the United States.
"I think we had the perfect weather and perfect conditions," the Swiss added.
"We'll be happy to come back here hopefully in two years (for the Olympics)."