The 22-year-old Ticino native finished in one minute 22.86 seconds, 0.03 seconds ahead of Tina Weirather of Liechtenstein and 0.33 seconds faster than Austria's Anna Fenninger.
American Lindsey Vonn, making a recovery from a knee injury, finished fifth.
Gut leads the overall women's World Cup standings following her two victories at Beaver Creek, Colorado (downhill and super-G) and giant slalom at Sölden, Austria.
She is well-positioned to solidify her lead next week in competitions set before home fans at St. Moritz, in the canton of Graubünden.
Her latest first-place finish came a day after Patrick Küng, 29, won the Beaver Creek super-G on Saturday, to record the first Swiss triumph in a men's alpine World Cup speed event since March 2012.
Küng clocked 1 minute 21.73 seconds to finish 0 24 seconds ahead of surprise runner-up Otmar Striedinger of Austria.
The result marked the first win for Küng, a downhill and Super G specialist, who made his World Cup debut in Wengen in January 2009.
His previous best finish was a second place in the downhill in Bormio, Italy on December 29th 2011, following a third place in the downhill at Garmisch on March 10th 2010.
Striedinger, starting 45th, captured the first podium finish of his career.
Austrian Hannes Reichelt and Italian Peter Fill, who finished second and third in Friday's downhill, shared third place, 0.38 sec behind Küng.
Norway's Aksel Lund Svindal, who stretched his lead in the overall World Cup standings with his victory in the downhill on Friday, finished seventh, 0.61seconds behind the winner.
"I can't believe it. It's hard to take in," admitted Küng.
"I hope it will act as a spark for the Swiss team," he said.
"We are on the right path."
The last Swiss man even to mount the podium in a World Cup speed race was Beat Feuz with a second-place finish in a downhill at Schladming, Austria, on March 14th 2012.
Until Küng's triumph, Feuz was the last Swiss winner of a speed event with his triumph in a super-G at Kvitfjell, Norway, on March 2nd 2012.
Rounding out the upbeat news for the Swiss ski team, Marianne Kauffman-Abderhalden finished second in the women's downhill at Lake Louise on Friday.
The 27-year-old Saint Gallen native narrowly missed another podium finish on Saturday when she came fourth in a second downhill race.