Küng only learned he would be skiing in the biennial championship's marquee event on Friday.
Switzerland had six ski racers battling for just four spots in downhill so Friday's training run also served as their qualification race.
But the 31-year-old Küng claimed his first world title, leading the powerful Swiss to two podium spots as teammate Beat Feuz continued his comeback from a myriad of injuries by taking the bronze.
"It is incredible," said Küng, who posted his first World Cup win in a super-G race in Beaver Creek two years ago. "I had no mistakes and my skis went really fast," the native of the canton of Glarus said.
"I was able to achieve a smooth run down the course."
Küng finished 13th in Friday's training and the coaches determined that Silvan Zurbriggen was the odd man out.
Küng finished with a time of one minute, 43.18 seconds, just 0.24 seconds ahead of silver medallist Travis Ganong, of the US. Feuz was third in 1:43.49.
"To share the podium with Patrick Küng is amazing," said Feuz, of the Swiss who had four skiers in the top 11.
This is Küng's first podium in three world championship starts. His best previous finish at the worlds was a seventh in the downhill two years ago in Schladming, Austria.
Küng skied a near perfect run, topping an earlier performance by Feuz and then watching Ganong fall short.
"Today I told myself to relax and just have fun," Kueng said. "I was really charging because in the past years I didn't have good results so I said to myself 'Why not today'."
Ganong is skiing better than he ever has, taking bronze in the last World Cup downhill in Kitzbuehel just a month after he won his first downhill in Santa Caterina, Italy.
"This is the best moment of my career," Ganong said. "I had to learn how to conquer the nerves and excitement of the world championships."
He had a breakthrough performance in the Sochi Olympics last year, finishing fifth in the downhill.
"I didn't know I would be able to perform like that at Sochi," he said. "I was so close to getting a medal at the Olympics."
Feuz placed second in the World Cup downhill in Beaver Creek in December as he continues his comeback from a series of knee injuries which kept him out of the 2008, 2009 and 2013 seasons.
"Two years ago not many people, including myself, would have bet the odds on me being here," said Feuz, who has had 11 operations on his left knee.
"This is an incredible feeling to stand on the podium in third place in a world championship downhill," he said.
American Steven Nyman finished fourth with a time of 1:43.52 while France's Guillermo Fayed rounded out the top five in 1:43.57.
Defending champion Aksel Lund Svindal, who was making just the second start of his season following foot surgery, placed sixth in 1:43.63 and reigning Olympic champ Matthias Mayer finished 11th in 1:44.10.
World Cup overall points leader Kjetil Jansrud finished 15th in 1:44.17.
Like the Swiss, the Americans had a superb day placing three skiers in the top ten.
Bode Miller was unable to compete in the downhill Saturday after he underwent surgery to repair a torn hamstring tendon resulting from a crash in the super-G.
The 37-year-old told NBC television that he in "leaning" towards retirement.