Vu started the day four shots back but marched up the leaderboard with five birdies - including two on 17 and 18 - and one bogey, carding a four-under par 68 for a winning total of 10-under 278.
She waited nervously on the sidelines as previous leader Yin (72) let the affair slip to a tiebreak with a pair of late bogeys.
Yin did not put up much of a fight in the playoff as her second shot hit the water and Vu, who collected her first title on the tour at the Honda LPGA Thailand in February, held her nerve to drain a long birdie putt for the win.
"I can't even put into words what I was feeling - I was nervous, I was scared, I was cold," Vu said in a televised interview
"I just wanted to hit the putt."
Vu, who had considered quitting the sport only a few years ago, was overcome with emotion after securing the win and said it was validation for the struggles she faced in her career.
"Everything happens for a reason, all the bad things," said Vu.
"I had a pretty tough - not easy - past two days. I was definitely my own enemy and I don't know how I pulled this out."
It was bitter disappointment for Yin, who started the day at the top of the leaderboard with compatriot Allisen Corpuz (74) and had the outright lead through 13 with a near-flawless performance at the Jack Nicklaus designed layout.
But the victory slipped through her fingers as she hit the bunker on 16 and 17, bogeying both holes, and she never regained her nerve for the playoff.
"Just wasn't hitting it very good. Honestly, I held it together, and then 16 and 17 really just was like bad club decision," said Yin.
"Obviously in the playoff hole, I just didn't hit a good shot. It just kind of spoke a lot about today."
Players adapted to fresh territory at the year's first women's major, as the tournament kicked off in a new home after some five decades at Mission Country Club in Palm Springs.
American Nelly Korda drained an eagle putt on 18 to finish third, one shot back, after missing the tournament a year ago following surgery for a blood clot in her arm.
The Olympic champion and 2021 Women's PGA Championship winner will retake the top of the world rankings after Sunday.
"Every single time I can finish well at a major, put myself into contention, that's what I strive to do," she told reporters.
"I have a lot to work on, but for it to be the first major of the year, I think I played pretty well, and hopefully I can build on it."