The 23 year-old produced a majestic display to record an incredible score of 95.25 in her second run and overhaul Finland’s Enni Rukajarvi, who took silver.
Great Britain’s Jenny Jones claimed the bronze thanks to a second run score of 87.25, which contributed its own page to the history books, as it gave the British their first ever Olympic medal on snow.
Anderson appeared some way off gold after her first run despite a respectable score of 80.75, Czech Republic’s Sarka Pancochova setting a marker with a fine performance that saw her score 86.25 to lead at the halfway stage.
A dramatic series of second runs saw Jones, who was positioned fifth after her first outing, set an early pace with a cleanly executed run embellished with some nice tricks that scored her 87.25.
A subsequent fall by Pancochova left the British athlete sitting in the gold medal position with eight runners remaining.
Rukajarvi, whose first run had put her in fourth place, claimed the lead with an exceptional 92.5 that looked good enough for gold, but a dazzling performance from Anderson included three near-flawless jumps to secure a superb victory.
The 23 year-old’s gold was the USA’s second in two days after Sage Kotsenburg’s triumph in the men’s slopestyle.
“At the top I felt nauseous and I felt sick,” said a delighted Anderson. “I thought 'let's go through what I'm more consistent with' and it paid off.”
An amazing feeling
"It feels amazing. There was so much anticipation and pressure leading up to this event for all of us," she added.
"To have that moment come so quick and know this is your moment to shine and be your best and show the world what a fun sport snowboarding is.
"And all the love up there, you don't see a lot of other events and sports where the girls are such good friends and really, truly support each other and give each other energy to really be their best."
Jones held onto third place after hotly-tipped Austrian Anna Gasser landed awkwardly on her penultimate jump, to earn Great Britain its first medal at Sochi 2014, and first ever on snow.