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Zoi (16) qualified for the final earlier this week, coming in as the fifth best qualifier.
After finishing the first run today in seventh place with a score of 65.50, Zoi landed a big switch backside 900 to card 92 in her second run.
That performance moved her up to third, behind US boarder Jamie Anderson and Austria's Anna Gasser.
Zoi crashed in her final run trying to land a frontside 1080 but her combined first two runs were enough to secure third.
Gasser landed a huge final run to pip Anderson for gold.
Zoi is the first Kiwi athlete to win a medal at a Winter Olympics since skier Annelise Coberger won a silver at the Albertville Games in France in 1992
After qualifying this week Zoi said she wanted to ''show the world what I've got'' in the final, NZME reports.
"Hopefully I can try some stuff and hopefully if everything goes well on the day, we'll see where that puts me. I want to show the world what I've got.
''It's really cool to be part of women's snowboarding because it's just progressing so much."
- additional reporting Otago Daily Times