Green denied South Koreans Sei Young Kim and Jin Hee Im with a birdie on the first play-off hole after rallying from six shots behind during Sunday's final round.
The world No.8's stunning victory adds to her LA titles in 2023 and 2024 and was Green's fourth win in her past five starts this year.
With a blazing five-under back nine, Green closed with a four-under 68 to reach 17 under for the tournament before claiming the $US712,500 ($A996,000) winner's cheque with a brilliant 20-foot birdie putt on the 18th green.
With her eighth LPGA Tour victory, Green joins Rachel Hetherington in joint-fourth place all-time among Australians, behind only fellow major-winning greats Karrie Webb (41), Jan Stephenson (16) and Minjee Lee (11).
Her latest triumph continues Green's extraordinary affinity with the LA Championship.
The Perth ace also finished runner-up in 2022, tied for third in 2021 and was equal ninth last year and she has fired 22 of 24 rounds in the 60s in the last six editions.
The LA three-peat follows a hat-trick of successes this year at the HSBC Women's World Championship in Singapore on the LPGA Tour and the Women's Australian Open and Australian WPGA.
The 29-year-old is unquestionably the hottest player on the planet entering the first women's major of 2026, the Chevron Championship, starting in Houston on Thursday.
Green is the first Australian since Webb in 2014 to win multiple times before the year's opening major.
After starting the day two shots off the pace, Green ambled through her first 10 holes in one over par to slip six back after overnight leader Kim eagled the 11th.
But with a brilliant burst of five birdies in six holes, courtesy of some majestic iron play, Green pulled back to within two strokes of the lead down the stretch.
Kim benefited from a huge break on the 16th, her wild drive left ricocheting off a tree and back on to the fairway.
Undeterred, Green set up a five-foot eagle try with another sublime approach but missed her chance to claim a share of the lead, settling instead for her fourth consecutive birdie to edge to within one of Kim.
"I thought the putt that I missed on 16 was the crucial moment," Green said.
"So I'm just fortunate enough that I at least got into the play-off, and I had that putt with a very similar line in regulation, so I felt somewhat comfortable.
"But it still was a tough putt, so I'm just really glad it went in the hole."
When Kim bogeyed the 17th after being unable to save par from the bunker, suddenly Green was in a three-way tie for the lead. Im had carded a Sunday 67 to post 17 under in the clubhouse.
In a magical display on the greens, Im needed only 25 putts in her five-under round to make the play-off.
The 27-year-old might well have won outright had she not been penalised one stroke for slow play on Saturday.
Kim had been eight shots clear of the field on Saturday but ultimately paid the price for only managing a final-round 70.
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