Anirban Lahiri of India and Joaquin Niemann of Chile, both making their debuts in the contentious Saudi-backed series,
also competed in the three-way playoff, with Johnson emerging victorious.
At International Golf Club, all three players achieved a 54-hole total of 15 under par.
On Sunday, Johnson shot a five-under par 65, giving him a lead of 15-under after making his sixth birdie of the day at the 13th.
In his LIV Golf debut, world number two Cameron Smith, the defending British Open winner, shared for fourth place with England's Lee Westwood.
Westwood surged into contention with an eight-under par 62 but bogeyed his final hole to miss the playoff.
Johnson became the first American to win the series' individual trophy after finishing eighth in the opening LIV Golf competition in London, fourth in Portland, and third in Bedminster.
His 4 Aces team finished two strokes ahead of Lahiri's Crushers, and he took home a $4 million first prize as well as $750,000 as his share of the team first prize.