Kilde attacked the Birds of Prey course and finished in one minute and 42.09 seconds, edging out Odermatt of Switzerland by 0.06 seconds. Canada's James Crawford (25) was third.
Kilde also topped the podium at Lake Louise last weekend and now has eight World Cup titles to his name.
"It has been a tough week," Kilde said.
"I caught the flu in Lake Louise after a nice weekend. It hit me really hard. I skied in clothes to have no sweat and take down everything a notch. I felt way better yesterday and that was fantastic.
"I still felt it a bit today but had enough strength for the two minutes I needed."
Kilde is second in the overall cup standings, 60 points behind reigning champion Odermatt, and will be back in action for the super-G on Sunday but must again contend with the Swiss.
"Marco Odermatt is the one thing that may stop me from winning," Kilde said with a laugh.
"And also there are a lot of contenders at the start and it is never easy to win races."
Odermatt, who won the Super-G in Lake Louise last week and is favoured to do so again on Sunday, is still searching for his first World Cup win in downhill.
"It is a little bit sad when it is just six-hundredths and you know where to find them but that is ski racing. I am really happy with my second place," said Odermatt, who had to contend with windier weather during his run.
"The conditions were very tough. I think it was not a super fair race today with the wind on top. For the first guys it was okay but the later are skiing well and they had no chance," he said.
"That is a little bit sad. But that is our sport."
