He was ultimately overhauled in the third and final run, however, by runner-up American Nick Goepper and bronze-winning Canadian Alex Beaulieu-Marchand, despite another impressive score of 90.00.
"First run I did what I planned to do, what I wanted to do as well as I could, and it held up against all the great runs today", said Braaten, who with this gold finally converted the promise he has shown at the X Games, where he has filled each of the podium's three steps the past three years.
Sweden's Oscar Wester, whose event-best 95.40 points led the standings after the qualification round, finished in 11th with a top three-run score of just 62.00 in the final.
"I know he's happy to have just been here and to have made it into the finals", Wilkas said.
"Before my last run, I was visualizing myself landing the last jump, arms open, screaming", said Goepper, a silver medalist this time around after Sunday's men's ski slopestyle final.
Now, the 23-year-old has his sights set on Beijing in 2022. "There were some really good guys still to drop, so it was a nail-biting moment waiting at the bottom".
The ski slopestyle field delivered an excellent standard in qualifying, with eight of the 12 athletes who reached the final having scored over 90.
Beaulieu-Marchand, 49th in the World Cup rankings, was a surprise bronze medallist, his 92.40 second run leaving him looking stunned as he stood on the podium.
Braaten set his leading position with 95.00 points in the first run, an intact score throughout the competition.
Woods' finish was one better than he managed in Sochi four years ago but it will come as no consolation to the Sheffield star who came to the Games as a strong medal contender.
"And Izzy (Atkin) came away with some hardware".