The 31-year-old held his nerve at the last to score a brilliant 97.75 points and snatch the title from Japan's Ayumu Hirano, who was leading on 95.25, with Australia's Scotty James third on 92.00.
It was particularly satisfying for White, known as "Flying Tomato" because of his red hair, who won gold in 2006 and 2010 and helped put the hipster sport on the map, but flopped in Sochi four years ago.
White said it had been an agonising wait for his score from the judges to come through, as he pipped Hirano to the title to make US history.
"Oh man, that was awful and amazing at the same time. I knew I did a great ride and I was proud of that and I could walk away with my head high, but when they announced my score and I'd won, it crippled me," he said.
"I was so overwhelmed with happiness, I've been through so much to get here. I had this crazy injury in New Zealand (in October) where I busted my face open.
"I actually did the same trick that injured me here in the halfpipe today. So there were a lot of obstacles to overcome and now it's all worth it."
'I'm still shaking'
Japan's Hirano had to settle for a second silver in a row and James, a two-time world champion, saw his victory hopes dashed as he fell on his final effort.
Team USA are threatening to clean up in snowboarding in South Korea, winning all four competitions so far.
The 17-year-olds Chloe Kim and Red Gerard, and fellow American Jamie Anderson, have all won in Pyeongchang, where competitors have struggled with blustery winds.
White, a comparative veteran and snowboarding's biggest star, was in ominous form in qualifying on Tuesday as he topped the standings with 98.50.
He has been determined to show snowboarding's next generation that he is no spent force after scoring a controversial perfect 100 in Colorado last month that sparked accusations of favouritism.
White called his winning run in the tricky conditions in South Korea "one of the most challenging I've ever done" because of the combinations he pulled off.
His watching family were "beside themselves", he said.
"I'm still shaking, I don't know what's happening.
"Man, three gold medals. My fourth Olympics. Thank you, I'm feeling blessed."
Scott Blackmun, chief executive of the US Olympic Committee, paid tribute to the America's Winter Games champions over the years, starting with speed skater Charles Jewtraw at the inaugural edition in 1924.
"Each and every one of the 100 times we have heard our national anthem play in Olympic Winter Games competition has been a truly unique and special moment," Blackmun said in a statement.
"These medals have spanned nearly 100 years and showcase the dedication to excellence that is central to Team USA and the entire US Olympic family."