Green birdied the last three holes and drained a pressure-cooker 30-foot uphill putt at the 72nd on Sunday to snatch victory from would-be world No.1 Celine Boutier.
The 27-year-old closed with a third straight five-under-par 67 to win by a shot at 13 under from Boutier, the French world No.3 who would have usurped American Lilia Vu for the top ranking had she won.
Boutier also carded a closing 67.
Green, the 2019 US Women's PGA champion, joins Karrie Webb, Jan Stephenson, Minjee Lee and Rachel Hetherington as only the fifth Australian to win at least five times on the LPGA Tour.
Her latest triumph also served as redemption of sorts after Green had previously suffered a heartbreaking runner-up finish at Sentosa GC.
"A few years ago, I almost had this trophy in my hands and made two bogeys coming down the last (stretch), so it's almost like it was meant to be today for me holing those two putts on the last two holes," Green said.
"I'm so happy to have this in my hands."
Such a dizzy scenario looked unlikely until late in the day.
After starting the final round two shots behind Ayaka Furue, Green birdied the ninth hole to reach the turn in a four-way tie with Japan's third-round leader, Boutier and American Andrea Lee at 10 under.
She fell two strokes adrift after taking three shots from the fringe and making her only bogey of the day at the par-4 10th as Boutier moved to 12 under.
But just as she did in winning her fourth LPGA Tour title at last year's JM Eagle LA Championship, Green hit the go button late with some inspired, clutch golf.
"I knew that I needed to go low today in order to win because the conditions were a little bit softer today than the last few days," the champion said after being soaked in champagne by compatriots Grace Kim, Sarah Kemp and Steph Kyriacou on the 18th green.
"But I was talking to my coach on the phone last night, and he's like, 'Yeah, try and get as many birdies in early as possible'.
"So I like to make things a little bit interesting."
As well as soaring into the top 10 on the LPGA's season-long Race to Globe points list, Green follows Webb, the nation's most prolific major championship winner, as a victor in this prestigious $US1.8 million, no-cut tournament.
"I've always loved coming to Singapore, even though it's a bit more hot than what I'm used to in Perth," she said.
"I love it here. I love the food and the fans have been amazing. I certainly felt everyone supporting me the last couple of holes."
Kim finished tied for 25th at one under after posting a disappointing Sunday 75.
World No.5 Minjee Lee rallied with a final-round 71 to share 29th at even par in her first event of the year - and first since switching from Srixon to Callaway, which forced an off-season swing tweak.
