The 16-year-old Mogul Skier recorded career best turn scores to narrowly miss out on the 16 woman Dual Mogul final.
Finishing just behind Cox was NSWIS team-mate Nicole Parks in 26th, also a personal best World Cup performance.
NSWIS Mogul Skiing Head Coach Peter "Toppa" Topalovic was very happy with the performance of his female athletes.
"Britt's turns were without a doubt the most impressive aspect of her run," Topalovic said.
"She has worked hard in this area over the past twelve months since the Vancouver Olympic Winter Games, and it's great to see her rewarded."
"Nicole also had a good run, and like Britt made some small mistakes which they are both capable of improving on in the next event."
In the men's event, Sam Hall was the highest placed Australian in 31st place with David Graham in 34th.
The event was won by Canadian athletes Justine Dufour-Lapointe and Alexandre Bilodeau.
The mogul team now heads to Lake Placid, USA, for the next round of the FIS Freestyle World Cup which will take place next weekend.