Austrian Hannes Reichelt finished second 0.06 seconds back for his fourth podium of the season, with Norwegian Aksel Lund Svindal, the World Cup downhill and overall leader, completing the podium after finishing 0.07 seconds off Küng's winning time of one minute, 32.66 seconds.
The legendary Wengen downhill, at more than 4.4 kilometres long, is the longest on the circuit but a significant slice of race-day drama was removed when strong winds near the top of the course forced a rethink.
Organizers shortened the course to 2.68 kilometres and dropped the start from 2,315 metres in altitude to 1,900 metres — although that did not stop much of the field hitting in excess of 150 km/h on the fastest section of the Lauberhorn.
Perhaps because of those changes, a number of big names failed to shine on a bumpy course which, in the past, has often rewarded the sport's all-rounders.
Swiss veteran Didier Defago narrowly avoided crashing into the safety netting while former two-time Wengen winner Bode Miller of the United States missed a potential podium place after a huge mistake near the bottom.
Austrian Max Franz then took the provisional lead in a time of 1:32.90, but two racers later his celebrations ended when Küng completed the course 0.24 seconds quicker.
Franz eventually finished just off the podium in fourth, with Miller fifth.
Canada's Erik Guay, a former world champion, did not finish while Italian duo Peter Fill and Werner Heel, who had both shone in training on the longer course on Wednesday, finished seventh and 15th respectively.
For the 30-year-old Küng, the victory marked a continuation of some good form this season after he won his first World Cup race, a super-G, in Beaver Creek in early December.
"Since I was a kid, I've been watching this race," Küng said.
"My first dream was to race it and my second dream was to win it," he said.
"Sochi and the Winter Olympics are a big event, but a Swiss winning in Wengen is also a big deal for us."
Küng only made his World Cup debut in 2009 never having broken into the ultra-competitive Swiss ski team for the world championships and Olympics.
But his showing did not come out of the blue for teammate Defago.
"It might come as a surprise to the wider public, but not to us on the Swiss ski team," the veteran said.
"He's been training well."
Svindal's third place saw the affable Norwegian further extend his lead atop the overall World Cup standings to 757 points, with Austrian Marcel Hirscher in second (675) and American Ted Ligety in third (433), the latter two not having taken part in the downhill.
Svindal also remains in top position in the downhill standings with 360 points, ahead of Reichelt (260) and Küng (221).