Clark waited until the last run of the final to clinch the host nation's first gold of this Winter Olympics.
She scored 47.9 points on her second run to snatch the lead from Frenchwoman Doriane Vidal, who took silver with her first-round 43.0.
"It's really cool to give people something to have pride in
and be happy about for a change"
Switzerland's Fabienne Reuteler held on with her initial score of 39.7 to secure bronze.
"It's really awesome," said Clark when asked how she felt about winning the first gold medal for the United States.
"It's really cool to give people something to have pride in and be happy about for a change," she said.
Former world junior champion Clark was lying second behind Vidal after the first run.
But the 18-year-old, who was the only one in the top five to improve on her second run, then sealed victory with the best mark of the day.
Her run included a maneuver called a McTwist, a 540-degree inverted spin, and a 720-degree jump at the bottom.
A partisan crowd cheered her on as Clark snowboarded to victory with the Guns 'N' Roses song "Welcome to the Jungle" blaring in the background.
But it was a disappointing day for 1998 Olympic champion Nicola Thost, who could only muster an 11th place.
Austrian Nici Pederzolli, who grabbed a wild card berth due to her place atop the World Cup standings this season, failed to make an impact and finished seventh.
Britain's hopes of grabbing a medal in the half-pipe event ended when Lesley McKenna was eliminated in the qualification stages.