But Swiss celebrations were tempered after Odermatt's team-mate Mauro Caviezel suffered a horrible crash and had to be taken to hospital.
After Kilde won the first downhill of the season on Saturday, Odermatt stopped the Norwegian from making a flying start in the overall standings with a fine run.
Odermatt, sixth out of the hut, came down in 1:32.53 with his speed in the tricky second sector proving decisive.
The victory is Odermatt's fifth in super-G on the World Cup circuit and his 13th overall and follows up on his third place finish in Saturday's downhill.
On a day which saw the favourites show their quality, Austrian Matthias Mayer - Olympic gold medallist in super-G - finished third, 0.78 behind Odermatt's winning time.
Fellow Austrian Vincent Kriechmayr was fourth with France's Matthieu Bailet tied for fifth with German Andreas Sander.
The race was halted when Caviezel crashed badly, bouncing down the piste before hitting the safety netting with force.
Caviezel lay motionless for several minutes before he finally stood up, looking shaken and showing signs of injury to his face.
"I'm glad I saw him standing," said Odermatt, who had watched the incident from the finish area.
"Once again we have seen what fine margins there are and how emotionally connected it is for us," he added.
"First me with a great ride, then a small mistake and there is a nasty fall. The first information from Mauro is reassuring. But then the result becomes irrelevant.
"My run was almost perfect. The long break didn't make it any easier for the competitors. My performance was great, it was one of my better super-Gs I've ever shown," he added.
Caviezel had suffered a head injury in a fall during training in January 2021 and had not skied in the World Cup since until this weekend.
