Kotsenburg won the men's slopestyle snowboarding competition and shortly afterwards Marit Bjoergen became Norway's most successful female Olympian by taking the cross-country skiathlon.
Ski veteran Miller, who won gold, silver and bronze at the 2010 Vancouver Olympics, was fastest in training for Sunday's medal race up in Rosa Khutor.
But he left no-one in any doubt as to his thoughts on the course, delivered in his usual forthright manner.
"This course is very treacherous. It has teeth everywhere," the 36-year-old said after his teammate Marco Sullivan almost crashed out in spectacular fashion.
"It looks like an innocuous place, there's nothing there but he almost killed himself. If that crash doesn't go just the way it went, he goes flying through the nets going 75 (mph) into the trees," Miller said.
"If you're not totally focused and paying attention, this course can kill you."
Kotsenburg, who only just squeezed into Saturday's final, claimed the inaugural slopestyle title on a course that has also witnessed a series of spectacular falls and bone-crunching injuries.
His first run scored 93.50 and although some of his rivals put in high scores on their second runs, the 20-year-old from Utah held on for victory.
"I'm really excited. It feels awesome. I dont know what to call it," said Kotsenburg.
Norway's Staale Sandbech (91.75) claimed silver while Mark McMorris of Canada took bronze with 88.75.


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