Odermatt beats Kilde to men's downhill gold
Odermatt, racing with bib number 10, laid down the challenge with a blistering run in one minute 47.05 seconds down the French resort's daunting L'Eclipse piste and Kilde, starting 15th, could not match it.
The Norwegian, who also had to settle for silver in Thursday's Super-G while Odermatt missed out in fourth place, crossed the line with a time 0.48 slower than the overall World Cup leader.
Canada's Cameron Alexander took the bronze medal after starting 20th.
"It's a crazy day, a crazy week," said Odermatt, who has been duelling Kilde all season in the World Cup and had a knee scare last month.
"It wasn't easy the last days after the disappointing super-G but I knew the skiing is here, the chances are here and I definitely went all in today because I knew I have to... it was a perfect run.
"It's just unbelievable that it worked today."
The gold was also a first senior world championships medal for 2022 Olympic giant slalom champion Odermatt, who has finished second seven times in World Cup downhills without winning one.
He was the first Swiss to win men's downhill gold since now-retired Beat Feuz in St Moritz in 2017 and the victory completed a downhill double for the country, with Jasmine Flury winning Saturday's women's race.
The Swiss knew he had done something special when he looked up at the timing screen at the finish, throwing his head back and roaring in delight with his arms pumping and ski poles thrust aloft.
Kilde had won five World Cup downhills before the championships but his hopes of becoming the third Norwegian male skier to win the downhill gold quickly disappeared.
Quicker at the first split, he then fell 0.11 behind Odermatt's pace and the gap widened steadily through the sectors.
"I did my best, a couple of turns I messed up a bit up top and in the middle," said the Norwegian.
"A hungry Odermatt is really hard to beat.
"I tried to charge and being one of the favourites I just focused on my skiing and nearly nailed it but not quite as (well as) Odermatt. I gave it a battle and I'm happy with that."
Alexander pushed team mate and super-G champion James Crawford out of the medals, the latter subsequently demoted to fifth by Austrian Marco Schwarz.
"I had a couple of mistakes but they weren't too costly," said Alexander. "I was kind of yelling at myself at the bottom to, like, hold on."
Reigning world champion Vincent Kriechmayr of Austria finished 11th.