Kueng secured the Swiss team's first victory since late in the 2011-12 season with a time of one minute, 21.73 seconds on the Birds of Prey course.
Striedinger managed to finish second despite starting 45th, over 2-10ths of a second back.
He was followed in third by countryman Hannes Reichelt and Italian Peter Fill, who were tied.
Reichelt reached a World Cup podium for the second time this weekend, and 25th time in his career. He was second in Friday's downhill, one spot ahead of Fill.
Ted Ligety of the United finished fifth in Saturday's race, one of his best ever super-G results. He will be the race favourite in Sunday's giant slalom, after having won seven of the last nine World Cup races in the discipline.
Canada did not enjoy the same success in the super-G as Friday's downhill, when Jan Hudec and Manuel Osborne-Paradis finished in the top 10.
Calgary's Hudec was tops on the team in 13th place in Saturday's race, with young Morgan Pridy of Whistler, B.C., in 24th. Osborne-Paradis of North Vancouver, B.C., ended up 27th, three spots ahead of Erik Guay of Mont Tremblant, Que.
Aksel Lund Svindal, who won Friday's downhill, was seventh.
American Bode Miller, who didn't compete last season due to a knee injury, was 14th, two places ahead of last year's overall World Cup champ, Marcel Hirscher of Austria.