A seemingly serene first run came undone when Woods failed to land the final jump, which consequently saw the 26-year-old suffer a cut to the chin.
"It feels unbelievable to win", Braaten told reporters.
"I know he's happy to have just been here and to have made it into the finals", Wilkas said.
American rider Nick Goepper came to the party late after missing on his first two runs, scoring 93.60 on his last attempt that included a huge final-air 1440 of his own.
Speaking after the final, Goepper said he changed his initial plan once the high quality of the field became evident.
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.
The 23-year-old Hidden Valley native earned scores of 59.00 and 69.00 in his first and second runs, respectively, at Phoenix Snow Park in Pyeongchang, South Korea.
"I knew that the calibre of my third run would put me in the top three".
Woods, who defied injury to finish fifth in Sochi four years ago, qualified for the final in eighth place in handsome conditions at Phoenix Snow Park, but crashed heavily on the last big jump of what could have been a medal-contending first run.
The event was ultra-competitive from start to finish - eight of the 12 qualifiers for the final scored more than 90 points. He placed second in the same event this year.
Compatriot Izzy Atkin won bronze in the women's ski slopestyle on Saturday.