Odermatt, the four-time reigning World Cup overall champion and 2022 Olympic giant slalom gold medallist, attacked the formidable Birds of Prey course to finish in 1:29.84, 0.30 ahead of American Ryan Cochran-Siegle and 0.69 ahead of Norway's Adrian Smiseth Sejersted.
"I'm very happy to win for the first time here in the downhill. I felt really good while skiing," said Odermatt, who had finished runner-up twice in downhill at Beaver Creek.
"The piste was very good from my side. Yeah, it was a cool race for me," he said after notching up his 48th career World Cup win.
"Every victory is special because it is always hard work to really go for it. But today, with the perfect weather we had, it was just nice to ski and fully trust your skiing."
Odermatt already has World Cup wins this season in the giant slalom and Super-G.
Cochran-Siegle, the 2022 Olympic silver medallist, claimed his fourth World Cup podium and first on American snow, while Sejersted was a surprising third after finishing 22nd at Beaver Creek a year ago.
Slovenia's Rok Aznoh crashed hard during his run and appeared unconscious before eventually being taken down the hill in a sledge.
Thursday's downhill race was moved forward a day due to the incoming bad weather. The Super-G will run on Friday before a large snowstorm is expected to arrive on Saturday, which could drop up to 30 centimetres of snow over the weekend.
