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Going third last in what had been a low-scoring contest on an intimidating course at the Rosa Khutor Extreme Park, the 23-year-old laid down a superb solid run to score 95.25 and blow away the competition.
Enni Rukajarvi won a surprise silver for Finland with the only other run to break through the 90-point barrier (92.50), and Jenny Jones took the bronze with 87.25 to become Britain's first Olympic medallist in a snow event.
Anderson's victory gave the United States a sweep of the first two gold medals in snowboarding slopestyle after Sage Kotsenburg won the men's event on Saturday.
"It feels amazing, goodness," Anderson told reporters.
"To be here and represent my country, and just everything that has to do with the Olympics is such an honour and I'm so grateful right now."
There was also a reminder of the dangers of the sport when Sarka Pancochova, who had led after the first run, botched a jump and landed with a sickening thud on the snow.
The 23-year-old Czech appeared to lose consciousness as she slithered down the slope before being helped to her feet and making her way groggily to the bottom, where she showed her rivals a huge crack in her helmet.
That came two runs after Jones had taken the lead with her second run, which she executed without error over the rails and three big jumps that had brought so many snowboarders down to earth with a bump this week.
"It was very much about clean landings, no hands down and grabs," said Jones. "I guess we started to see that's what (the judges) were after and it was important to do everything the best you possibly could."
Rukajarvi went out straight after Pancochova's tumble and her nerveless run put her top of the leaderboard until Anderson, who had botched a landing in her first run, carved and jumped her way down the course.
"I was third to last so I watched almost all the second runs and I was really just trying to just stay calm and kind of just reserve my energy," added Anderson, who said she had prepared for the final by listening to yoga tapes and lighting candles.
"It was a lot of stress up there, the outreach that this event connects to across the whole world is just out of control.
"I was just trying to keep it light, I was freaking out."
Jones then had a nervous wait to see if any of the final two competitors could knock her off the podium.
The most likely was the final competitor, Anna Gasser, who had set the best score in qualifying.
Perhaps unsettled by the farcical scene at the start of her first run, when she set off too early but was unable to scramble back up the icy slope, the Austrian could only manage the 10th best score of the day and Jones had her medal.
"I feel very proud to have got a medal for my country, something I didn't feel was a possibility for me," Jones said.
"It was only two years ago we found out our event was going to be in the Olympics, until then I never represented my country."
Torah Bright has already won one Olympic gold for Australia but came up short in her bid for three snowboarding medals in Sochi, finishing seventh after failing to land a clean run with her more complicated routine.
I am so proud of the United States they are bringing home all the Gold!!!!
The Politicians will have somewhere else to turn now, think the turnip is out of Blood dealing with the masses.
It won`t be ALL the gold.. And to think ALL is dreaming...I`m an american and love our olympians but I admire all who do the best of the rest and get the gold--silver and bronze...
Lets leave the trival bs @ the side of the road and praise the medal winners, they are champions in their sport.....regardless of their origin.
Staying upright is enough? OK congratulations
WAY TO GO JAMIE!!!!! GO USA
I'm really proud of Jamie! Way to go! I know it's not easy to do.
very bproud of you ,Jamie...congratulations.!!
Proud and Happy for you & all our USA team members!
USA on the way: Go Guys & Dolls.
dont you just mean dolls they seem to be the only ones that that get reported on but then teses days what else would you expect.
After all is said and done....I believe that as an American we should be very proud of our Olympic teams. I just pray that we as Americans will not be in harms way, with the unrest in several countries. Our metal winners, as we know, deserve all the glory they earn. It doesn't mean that we are snooty or stuck on ourselves. It means we've worked our butts off to be the best we can be. If that means a metal, then so be it. For the next Olympics I pray they choose a country that is in less of an upheavel.....Peace between countries for the Olympics should be heart warming instead of rivals against rival countries. The Olympics are for the world to come to peace within themselves for all the world!!
Thats where my quilt went
That's just wonderful and I am happy for them.