Kilde, also a winner in the downhill at the Swiss resort last year, stormed down the Lauberhorn piste in a race shortened because of high winds to finish 0.88sec ahead of overall World Cup leader Odermatt.
Italy's Mattia Casse was third at 1.01sec behind World Cup downhill leader Kilde for his second career podium after Val Gardena last month.
The start of the race, the longest and oldest on the World Cup circuit, had been lowered over safety concerns in the Alps.
Kilde built his 19th victory on the world circuit, and sixth this season, after a storming start before finding the ideal trajectory on the winding "path", a sector where the slightest brake is very costly.
"I felt like I had good speed out of the tunnel and knew I had a chance," said the 30-year-old two-time Olympic medallist.
"If I came down with green numbers, then it was a good sign. It is working well with my equipment and skiing. I can keep working on that and gain more confidence."
Odermatt was chasing his first downhill World Cup victory.
The Swiss pulled out all the stops for a breathtaking finale having lacked the precision of his rival at the top of the piste with a slight mistake when landing the famous "dog's head" -- a blind jump between two rocks.
Nevertheless the 25-year-old is flying towards a second consecutive big globe thanks to his giant slalom supremacy, putting him 340 points ahead of the Norwegian, but is second in the downhill standings.
"Alex (Kilde) was once again incredible and by far the best today, so I am happy with the place," said Odermatt after his 13th podium of the season.
"I can find two or three tenths but not 0.88 so he deserved the win, and I will have to work harder."
Despite the skirmish between the two champions, once again sumptuous as they push each other to their limits, neither could compete in the applause metre with the darling of Wengen, Beat Feuz.
The local hero was enthusiastically greeted for his final appearance in an event he won three times -- 2012, 2018, 2020 -- with the reigning Olympic downhill champion taking fifth place at 1.25sec in front of more of 10,000 cheering spectators.
