Li, a 21-year-old Californian chasing her first title, had an LPGA record-equalling three eagles in her 11-under par 60 and had the clubhouse lead on 17-under 196.
But 31-year-old Thai veteran Jasmine recovered from an errant tee shot to eagle the 72nd hole and force the playoff with a 10-under round of 61.
It would be more than an hour before they returned to the par-five 18th, where Jasmine’s eagle putt was an inch short and they settled for matching birdies to start the playoff.
Off the tee of 18 again, Jasmine gained the edge when she found the fairway as Li hit into the left rough.
Jasmine’s second shot raced through the green and spun back and with Li trying to get up and down for birdie the Thai rattled in her eagle putt for the win.
“It’s been a long time,” said an emotional Jasmine, who claimed a third LPGA title but her first since the 2019 Dow Invitational pairs event. “There was a time that I thought I’m probably not going to win again.
“But today, everything just fell in the right place at the right time.”
Li became just the seventh player to post three eagles in an LPGA tour round.
The first was a hole-out at the par-four eighth, part of a burst that saw her pick up seven strokes in seven holes.
She had birdied the fifth and seventh, then birdied the ninth, 10th and 11th to seize a share of the lead on 12-under.
It was all the more unlikely considering she was one-over for the day after three-putt bogeys at the second and fourth.
Late magic
“I had honestly no clue that this was going to happen,” Li said. “I did not think I was in it at all. I mean, after two three-putts in the first four holes I was just like, I don’t know.
“And then some magic came and I shot 60. Even though I didn’t win, just this is the greatest thing.”
She briefly took the solo lead on 14-under with an eagle at 14, where a superb second shot left her a four-foot putt.
She drained a long birdie bomb from off the green at the 15th and had a two-shot lead after her eagle at the 72nd hole.
But first-round leader Jasmine was hot on her heels. After three front-nine birdies, she kept the pressure on with birdies at holes 10, 11, 13, 14 and 16.
Her chances of joining Li atop the leaderboard appeared to take a hit, however, when her tee shot at 18 sailed right and hit a cart path.
But her second shot from sparse rough left her a five-footer for eagle and she made it to complete her 61.
“Somehow it went straight, right at the pin,” she said.
South Korean Kim Sei-young carded a nine-under 63 for solo third on 197.
Overnight leader Ashleigh Buhai of South Africa and Thailand’s Arpichaya Yubol were both within striking distance on the back nine.
But Yubol’s challenge faded with a bogey at the easiest hole on the course, 14, where she hit her tee shot into the hazard left of the fairway.
She closed with a 66 to share fourth with Japan’s Mao Saigo on 199. while Buhai’s 69 left her in solo sixth on 200.
Suteepat reigns in Taipei
Elsewhere, Suteepat Prateeptienchai put the finishing touches to a classy wire-to-wire win at the Yeangder TPC in Taiwan on Sunday after signing off with a three-under-par 69 for a two-shot victory.
After a brilliant week of front running the 31-year-old Thai finished the US$1 million event on 21-under, holding off Asian Tour No.1 John Catlin, who claimed second place after a typically strong closing 65. The American had an explosive start, making birdie on his first five holes, reports the Bangkok Post.
Miguel Tabuena from the Philippines was outright third, one shot back, following a 70, while Lee Chieh-po from Taiwan was fourth, another stroke behind, after a 67, at Linkou International Golf & Country Club.
“I love Taiwan!” said Suteepat, whose other win on the Asian Tour also came in Taiwan, at last year’s Taiwan Glass Taifong Open - where he won by four.
“It was tough today, because of the wind and good players followed me. I saw Catlin’s score and then got nervous.”
He had a two-shot cushion at the start of the day and despite Catlin’s brilliant start he was in complete control until a wobble towards the end when he bogeyed 15 and 16.
With Catlin, playing two groups ahead, making a birdie on the par-five 18th, it meant Suteepat arrived at the last with a one-shot lead. However, any thoughts of the event going into extra holes where quickly dispelled when he found the front of the green in two and nearly holed his chip for an eagle before tapping in for a birdie.
“Got into trouble on 15 where I went over the green and then found a greenside bunker on 16. But I kept thinking I am still the leader, and I must hold on. This means a lot; an exemption for two years [on the Asian Tour] is amazing!”
It is only the second wire-to-wire win of the year, with Catlin having recorded the other at the Saudi Open presented by PIF.
The victory comfortably surpassed Suteepat’s best performance this year which was joint sixth in the Mandiri Indonesia Open in August, and he moves from 47th on the Asian Tour Order of Merit to eighth.
It also means Suteepat has impressively tasted victory again in just his second season on the Asian Tour. Last year was his first full season, after having earned his card by winning the 2022 Asian Development Tour Order of Merit, helped by three magnificent wins in Indonesia.
Catlin, also winner of the International Series Macau presented by Wynn this year and leader of The International Series Rankings, put the pressure on further by making birdie on the seventh and went out in six-under-par 30.
It’s no wonder Suteepat took notice, especially when Catlin made birdie on 10, but fortunately for the Thai leader the birdies dried up for the in-form American, who dropped his only shot of the day on 16 before one last throw of the dice with a birdie on the last.
“It was windy, it was difficult, it was rainy - I think we saw pretty much saw every possible weather out there,” said Catlin, winner of this event in 2016.
“I handled it pretty well; I guess all my years in Europe paid off today.
“I hit the ball much better today than I did yesterday and that gave me a lot more chances and I was able to convert a couple of them. I had a couple stone dead so that always helps. I just kept having fun and enjoying playing golf.”
He now has a huge 1,146.83 points lead on the Merit list over second placed David Puig from Spain. With nine events remaining it will taking something exceptional for someone to catch him.
Suteepat will have another chance to make the most out of his affinity for Taiwan this week as the Asian Tour stays in country for the Mercuries Taiwan Masters at Taiwan Golf & Country Club.