It was a World Cup personal best for Graham, who is competing in his first full season in the northern hemisphere series, as well as the first time this year that Australia was represented in the men's and women's moguls finals at World Cup level.
Graham's 10th place in the massive field of 73 competitors pushed his ranking up 13 places to 23.
"To achieve better results each week has been one of my main goals this season," he said.
"I've been trying to improve all my tricks and I think today's result showed that."
Cox also finished 10th in the women's event, her third top 10 after five rounds of competition and she sits eighth in the rankings.
"My skiing across the board is a lot more consistent so I have been able to improve each element of my skiing which has meant that I have been able to get into a few more finals and a few more top 10 finishes," Cox said.
Graham finished behind Canadian duo Mikael Kingsbury and Alex Bilodeau, with American Patrick Deneen taking the other podium placing.
The Utah resort will host dual moguls events on the weekend.