Kim, who stopped playing in 2014 amid alcohol and drug addiction, triumphed by three shots in a final-round duel with Rahm at the Grange.
The 40-year-old Kim, who has been sober for three years, fired a flawless nine-under 63 on Sunday to finish 23 under and overtake Rahm (20 under).
Rahm's forecast fight for the title with Bryson DeChambeau fizzled with the American drawcard flailing four bogeys in his first six holes.
Rahm and DeChambeau were 19 under co-leaders overnight but it was left to Kim, who started Sunday five shots adrift, to challenge.
Rahm could only shoot one under as Kim's redemption round featured a tournament-winning stretch of five birdies in six holes from the 12th.
The Californian - who holds the record for most birdies in a round at the US Masters (11); is a three-time US PGA Tour winner; and a Ryder Cup champion before his hiatus - fired nine birdies all up to collect the $US4 million ($A5.7 million) winner's cheque.
Kim, after a decade out, returned to golf in 2024 as a reserve on the LIV circuit, but lost his card at the end of last season.
He scraped back as a reserve via an international play-off and, this week, joined a LIV team for the first time - Dustin Johnson's 4Aces.
Kim admitted he was feeling blessed just to be alive, let alone contending in golf tournaments.
"It has been overwhelming," the father-of-one said.
"But I'm never not going to fight for my family.
"God gave me a talent. I was able to produce some good golf today, I knew it was coming.
"Nobody else has to believe in me but me. And for anybody that's struggling, you can get through anything."
Kim produced his Sunday best to eclipse Rahm as other challengers came, then went.
"I knew this was going to happen but for it actually happen is pretty insane," he said.
"I just want to thank all the people that have supported me ... who, when I was not playing well and I was struggling on the verge of never coming back to LIV, always supported me.
"Thank you to everyone that's been in my corner. I'm going to keep doing it."
DeChambeau finished 17 under, alongside Englishman Tyrell Hatton and American Peter Uihlein.
Australia's Lucas Herbert (16 under) and was, briefly, one shot adrift when Rahm was leader.
But Herbert's bid to become the first Australian to win an individual LIV title in Adelaide then crashed with three consecutive bogeys.
Fellow local Marc Leishman carded a fine seven-under 65 to finish 15 under, tied with compatriot Cam Smith, who shot 70.
Gold Coast-born Elvis Smylie, the 23-year-old who won the individual title on his LIV debut last weekend in Saudi Arabia, finished nine under.
The quartet's combined feats helped their all-Australian Ripper GC win the teams event.
Captain Smith's outfit, who also claimed the teams title last weekend in Riyadh, finished two shots ahead of Rahm's Legion XIII.
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