The former Japan Tour stalwart's putter was on fire in front of large, boisterous crowds at the par-72 Grange Golf Club to take a one stroke lead from New Zealand's Danny Lee and Mexico's Carlos Ortiz.
Chile's Mito Pereira, India's Anirban Lahiri and Americans Peter Uihlein and Andy Ogletree were a shot further back.
Last year's Masters champion Jon Rahm, playing the course for the first time after joining LIV this year, finished strongly with consecutive birdies to be four adrift and lurking as a major threat.
"Today my putter was really hot. I had some troubles here and there, but my putting was there to help me get through," said Kozuma, who is in his first year on the Saudi-backed circuit.
"It's my first time here and I wanted to play really well in front of my family and I got to do that."
Under LIV's shotgun start format, where 18 groups of three players tee off simultaneously on different holes, Kozuma began on the par-four 15th with a birdie and never looked back.
He went to the turn as the outright leader after six birdies on the front nine, with an eagle at his 11th propelling him into a two shot lead.
Lee, playing alongside Kozuma, overcame a bogey start to produce seven birdies in his next 11 holes before a sensational eagle from the bunker drew him level.
But the Japanese star responded with another birdie to hold off a charging pack, led by Lee and Ortiz, who mixed nine birdies with a bogey.
Rahm rolled in five birdies in six holes to race up the leaderboard, but stumbled with consecutive bogeys at the 14th and 15th before a strong finish.
"If I could have avoided those mistakes, it could have shaped up to be a really good round," said the Spanish former world number one.
"But I did the job and kind of bounced back and finished strong."
Fellow major winners Bryson DeChambeau and Cameron Smith, who both tied for sixth at the Masters this month, were five shots off the lead.
LIV supremo Greg Norman this week called Adelaide the blueprint that all other events should aspire to after a successful debut last season.
And the course was again heaving with fans lapping up the atmosphere.
The biggest cheers were at the par-three "party hole" 12th, crammed with 5,000 fans fuelled by alcohol and pumping music who got louder as the day wore on.
It was the scene of LIV's first-ever hole-in-one last year when Chase Koepka hit a perfect drive to spark raucous celebrations.
No one managed to repeat the feat, although Henrik Stenson and Tyrrell Hatton had the crowd on their feet when both went within a whisker.
At the 14th, Australia's Matt Jones, South Africa's Branden Grace and Belgium's Thomas Pieters all came within millimetres of an ace.
