By finishing third, the 20-year-old Olympic Winter Institute of Australia/NSWIS athlete becomes just the second Australian female World Championship moguls medallist, following on from Maria Despas' silver medal in 2001.
The outstanding result means that Australia has picked up two golds and a bronze in the first four days so far in these Championships.
Australia’s Scotty James pocketed the gold medal in the snowboard halfpipe a day earlier and aerial skier Laura Peel also took gold on Friday (Australian time).
Cox shared the podium with Canada’s gold medallist Justine Dufour-Lapointe and two-time Olympic medallist Hannah Kearney from the United States, who added a silver to her previous six World Championships medals.
Cox’s teammate Matt Graham finished in 16th place, which could have been a lot higher if not for a landing mishap on his second jump.
Nicole Parks finished in 29th place, after an off balanced landing after the first jump and a suspected knee injury during the qualifying run.
At the end of the six woman super-final on a day that Cox will never forget, she said that she was “stoked” by the way everything came together today.
Despite having a World Championships medal within reach at the start of the super-final, after qualifying in third, Cox strong state of mind shielded out all forms of pressure.
“I think what helped me today was that I was having so much fun. I was relaxed and I was confident,” she said.
“I trusted my training and I trusted the feedback I was getting from my coaches and that gave me confidence. So when I was in the start gate I just went for it.
“I had so much fun skiing my runs today,” Cox said.
“I had three runs which I was really, really happy with. It’s an excellent feeling when you cross the line when you are so happy with your runs.”
She added that she was particularly proud to stand on the podium with the Canadian and the American.
“To end up on the podium with Hannah and Justine, two Olympic gold medallist is very special. I have a lot of respect for these girls.
"I’m pretty excited to be on the podium with them.”
While Graham was hoping for a finish higher than 16th, especially with the knowledge that he was fresh from claiming a World Cup silver medal in Deer Valley a little more than a week ago, the OWIA/NSWIS athlete can be pleased with the way he skied.
Graham qualified in sixth place for the first final for the top 18 athletes and looked poised to attract a strong score when he was slightly deep when landing his second jump.
However Graham will have an opportunity to show how far he has progressed in the last 12 months when he competes again in 24 hours in the duals event.
The men's final was won by Frenchman Anthony Benna, who took home his first World Championship title, ahead of Canadian and favourite for the event Mikael Kingsbury. Russia’s Alexandr Smyshlyaev took the bronze.
IMAGE: Britt Cox celebrated on the podium at the World Championships © Peter Hogg