Australian Torah Bright won silver, giving Australia its first medal of 2014, followed by Kelly Clark from the U.S., who won bronze. Farrington scored a 91.75, just 0.25 ahead of Bright who had a score of 91.50.
"I can't really believe it right now. It is kind of -- I am if no man's land kind of," Farrington said.
During the first run, Hannah Teter of the U.S. was leading with a score of 90.5, but had to settle for fourth place after the second run.
Clark was expected to get the gold after having won 28 of the past 34 contests since Dec. 2010, making her one of the most dominant and successful snowboarders. But despite a fall in her first run, she made a comeback in her second to claim the bronze.