The 20-year-old slopestyle snowboarder was gunning to join Annelise Coberger, also from Christchurch, who won silver in the alpine skiing slalom at the 1992 Games in France.
Canada's Mark McMorris and Norway's Staale Sandbech overtook Garcia Knight on the second run, leaving the Kiwi in third.
Garcia Knight's podium place looked in initial trouble from Canadian Sebastien Toutant's third run until he came adrift at the end.
"On the last run I was really nervous I got a little bit overwhelmed. But to come fifth at my first Olympics, I'm relatively happy," Garcia Knight said after the event.
But American 17-year-old Redmond Gerrard put on a brilliant show to take the gold medal position, emulating countryman Sage Kotsenburg's surprise performance in Sochi.
Garcia Knight followed next, and he crashed early on his final run leaving him in fourth place at best.
Garcia Knight eventually finished fifth.