Australian star Torah Bright of Salt Lake City finished seventh, with two more Olympic events to come in the next week.
Anderson, who's from South Lake Tahoe, Calif., is regarded as the world's best slopestyle rider. But she found the Olympics slightly overwhelming.
"Heck, yeah," she said. "This is the biggest stage in the world ... definitely a little more stress and pressure."
She managed to calm herself with an evening ritual of music, candles and yoga, then went out Sunday and delivered two solid runs over the rails and jumps. In the format that counts the best of two scores, she stood second after the first heat. Anderson temporarily was overtaken during the second run while waiting for her turn, but she came through with a 95.25 score and ended up with a convincing victory over Rukajarvi (92.5).
"Just jumped out of my chair," Kotsenburg said via Twitter after Anderson's run.
Even though the Olympic showcase was unnerving, Anderson obviously welcomed slopestyle's introduction to the Games.
"It's such a fun, creative, unique sport," she said. "We all started this because of the fun it brings. It's like playing, you know?"
Bright had trouble landing one of her jumps in each run but was not overly disappointed. She'll defend her 2010 title in the halfpipe event Wednesday and join the snowboardcross competition next Sunday. Anderson gave her a big hug at the top of the course, illustrating the riders' bond that made Bright enjoy being part of the slopestyle event.
"It's a lot more relaxed than even halfpipe," Bright said. "And these characters I call them characters, because they're such fun-loving, genuine humans ... I'm so excited that the world can see a different side of snowboarding."