Johnson had entered into a three-way playoff with Chile's Joaquin Niemann and India's Anirban Lahiri after all three finished their 54 holes at International Golf Club on 15 under par.
Reigning Open champion Cameron Smith, making his LIV golf debut, finished a shot back on 14 under alongside England's Lee Westwood, who closed with a red-hot 62.
Johnson snuck into the playoff via a couple of crucial par saves at 17 and 18 before nailing an uphill 30-foot putt for eagle on the first extra hole after sending it racing up the hill on the green.
"Yeah, it was going a little fast, but it was a good line," he said.
"I felt like I played really well all week, I felt like I got some unlucky breaks here [the 18th] the first time around. It owed me one, and I got it."
Lahiri - wearing shorts after LIV Golf CEO Greg Norman's recent announcement that it was now permissable during tournament play - narrowly missed out on an outright victory after seeing his six-foot putt for eagle on the par-five 18th circle the cup and lip out.
Johnson's victory also helped his team, the 4 Aces, to a third consecutive team win. He, Talor Gooch, Pat Perez and Patrick Reed will split the $3million first place prize.
The arrival of the LIV Golf circuit has caused a lot of controversy, but Johnson said he is happy to be a part the new venture, and with so much money on the line, it still creates a lot of competitive tension.
"Especially with that check that you get - you can feel it," Johnson said.
The inaugural LIV Golf season is now officially halfway through its eight-event schedule, with stops in Chicago, Bangkok, Jeddah and Miami still to come before the end of October.