The two Canadians finished behind 17-year-old American Redmond Gerard, who gave the US its first gold of 2018 with a score of 87.16.
In doing so, Parrot nudged teammate Mark McMorris, of Regina, Sask., down to bronze to give Canada its first two medals of these Games.
Along with all Canadians, I am extremely proud of Max and Mark's outstanding performances.
Tyler Nicholson of North Bay, Ontario finished just off the podium and ended with a 76.41, which he scored in his second run.
Sebastian Toutant of L'Assomption, Que., was third in the first heat, earning 78.01 points in his first run.
For much of the third run in the event's final, which took place on Saturday evening local time, McMorris was holding on to second place with a best score of 85.20.
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Following a snowboarding accident a year ago, McMorris was fighting for his life after breaking 17 bones and suffering a collapsed lung and ruptured spleen.
"I had to change my run at the last minute and go with something a little easier but more safe", Parrot said.
Canada's Max Parrot reacts after completing his run in the men's slopestyle finals at Phoenix Snow Park in Pyeongchang, South Korea on February 11, 2018.
PYEONGCHANG, Korea, Republic Of-Max Parrot had the best run of the day as all four Canadian snowboarders qualified for the men's slopestyle final at the Pyeongchang Olympics on Saturday.
While they're both Canadians, the rivalry between Parrot and McMorris is undeniable. Toutant and Parrot had yet to put together clean runs. His score of 87.16 was just enough to slip by Parrot. The riders will each complete three runs, and the best score from each will determine the medals. With just two runs, "You land one, you're stoked, you don't and there's so much pressure".
"It's a duel that motivates me", said Fourcade, the 29-year-old French army officer.