Christensen scored 95.80 on a scorching first run to lead from compatriots Gus Kenworthy on 93.60 and Nick Goepper on 92.40. The closest challenger for the US medal trio was Norway's Andreas Haatveit, who missed out on a medal by six-tenths of a point, ahead of fifth-placed Briton James Woods, who was hampered by a hip injury.
"This is pretty crazy. It has been just an amazing day," Christensen said. "I am shocked. I am stoked to be up here with my friends. America, we did it.""
Christensen’s victory is something of a surprise, since the 22-year-old Utahn’s only win in a major competition came in 2011.
Two-time X-Games champion Goepper had come into the competition as the man to beat, but said he was delighted with bronze.
"I feel amazing. I think today was the best display of skiing we have ever seen in our sport, so I am so happy," he said.
The United States has won three of the four gold medals on offer in Sochi in slopestyle, a festival of tricks on rails and jumps. Americans Sage Kotsenburg and Jamie Anderson won gold in the two snowboard slopestyle events, before Canada’s Dara Howell saw off Devin Logan of the United States to win the women’s ski slopestyle Tuesday.
Slopestyle’s first Olympic showing has come amid controversy over the course, which was altered to lower the height of the jumps last week in light of a spate of injuries in training and complaints from snowboarders that it was unsafe.
Prior to Thursday's final, there had been two other podium sweeps by a single country at the Sochi Olympics, both of them by the Netherlands in men's speedskating.