Christensen, Gus Kenworthy and Nicholas Goepper won the gold, silver and bronze to give the United States' medal total a dramatic boost.
The first three golds for the Americans at these Olympics had all come in snowboarding.
Christensen turned in the best performance of the finals with his first attempt, receiving a score of 95.8.
Kenworthy jumped into the top three with his second effort, which brought a 93.6 from the judges. He had been in 10th place after the first run. Goepper's score of 92.4 came in his first trip down the course.
Slopestyle competitions have swept the world of winter sports with the athletes constantly coming up with new tricks to perform while riding down a steep slope into which rails and jumps have been built.
Slopestyle has become so popular that the International Olympic Committee put the competition into the Games for the first time in both snowboarding and freestyle skiing.
This was the fourth and last of the slopestyle events at these Games and the Americans took full advantage. The United States came away with a gold medal in both the men's and women's snowboarding slopestyle and a silver in the women's freestyle skiing slopestyle.
The only other times U.S. athletes swept the medals at the Winter Olympics came in men's figure skating in 1956 and in the men's snowboarding halfpipe in 2002.
American Bobby Brown, a four-time winner of gold at the X Games, also made Thursday's finals only to finish ninth.