The 29-year-old made the most of windy conditions in the Austrian resort, which forced the start of the race to be moved down the Streif piste to the Mausefalle jump, to clinch his sixth victory of the FIS Alpine Ski World Cup season.
Kilde is the first Norwegian skier to win the downhill in Kitzbühel since Kjetil Jansrud in 2015.
In the low cloud and with a storm moving in quickly, the Norwegian started quickly on the leader Matthias Mayer of Austria before gaining time in the flat of the Brückenschuss and Gschöss.
An aggressive line on the modified course, with slightly different turns to the normal, saw him just about squeak inside a gate he looked like he might miss, but Kilde kept his advantage to the line, crossing in 1 minute 55.92 seconds.
"I did my best, I had such a good run, it's an incredible feeling," Kilde said. "Standing here now just over a year after I had an operation on my knee, it's quite incredible.
"It's a lot of things that have to fit into place when you want to win here and today it's a good feeling.
"I'm quite speechless, Kitzbühel has always been my Achilles heel. I've been in shape before here and I've been sixth in the downhill. Today I wish there was 70,000 people here. But still, it's Kitzbühel and I'm more than proud and more than happy with today."
France's Johan Clarey was the surprise second-place finisher, having started with bib number 17.
The 41-year-old Clarey even found himself momentarily quicker than Kilde as he kept pace with the Norwegian's time for most of the course, finishing 0.42 seconds behind.
That pushed Mayer, the winner of this classic race two years ago, into third. Mayer did not have a perfectly clean run, having to overcome his skis turning unexpectedly on one of the jumps, eventually dropping to fourth.
Instead, starting 43rd – during a break in the storm which caused snowfall and bad visibility for the starters from 20th to 39th –, Clarey's French teammate Blaise Giezendanner scored a massive personal best third-place finish.
His 1:56.55 finish was 0.63 seconds behind Kilde and his first World Cup podium, having never finished higher than eighth previously.
Switzerland's Marco Odermatt was fifth, with defending champion Beat Feuz was eighth.
The results mean Kilde moves into the lead of the downhill World Cup standings, replacing previous red bib holder Dominik Paris, who drops to fifth.
Kilde leads Mayer by 53 points, while the two stay second and third in the overall crystal globe race behind Odermatt.
There was a special role for Marcel Hirscher, the retired two-time Olympic and seven-time world champion, as he served as a forerunner for the race.
A second downhill race is planned in Kitzbühel on Sunday.