Trailing world number one and overwhelming favourite Woods by two strokes overnight, Yang, ranked 110th in the world, kept his composure in difficult, swirling winds at Hazeltine National to fire a two-under-par 70.
He snatched the lead for the first time when he spectacularly chipped in from just off the green to eagle the driveable par-four 14th on the way to an eight-under total of 280.
Although Yang collected his second bogey of the day by three-putting at the 17th, he finished in birdie style, striking a superb approach over a tree to 10 feet at the par-four last and coolly sinking the putt.
He punched his right fist in celebration before raising both hands above his head to acknowledge the roars from the huge gallery packed around the 18th green.
"I have tried to master the art of controlling my emotions throughout my career and I think it turned out quite well today," a beaming Yang, 37, said in a greenside interview, speaking through an interpreter.
"I think it's going to be a bit of a crazy party for them, especially for all my friends," he added, referring to his supporters watching final-round coverage on television in South Korea.
Woods, in pursuit of a 15th major title but his first this year, missed four birdie putts from 12 feet or less to card an erratic 75 featuring five bogeys and two birdies.
BEST CLOSER
The 33-year-old American, renowned as the best closer in the game, stumbled to the finish line with bogeys on the last two holes.
Britons Lee Westwood and Rory McIlroy signed off with matching 70s to share third place at three-under 285.
It was the first time Woods failed to triumph in a major after holding at least a share of the lead after 54 holes, having accomplished the feat to clinch his 14 previous titles.
"I hit the ball so much better than my score would indicate," Woods told reporters after totalling 33 putts in the round. "I made absolutely nothing.
"I had a terrible day on the greens at the wrong time. I was in control of the tournament for most the day. I did everything I needed to do except put the ball in the hole.
"Y.E. played great all day," added Woods, who had been bidding for a third consecutive victory on the PGA Tour. "The only mistake he made all day was the one on 17. It was a fun battle."