Ben Campbell, a 34-year-old from Queenstown, and Rahm both fired extraordinary nine-under 63s at the Grange on Friday.
Rahm turns at 13 under after two rounds, with Campbell one stroke adrift.
The Kiwi's stunner featured an eagle - holing a 77-metre second shot on the par-4 18th hole - and seven birdies.
Rahm also bagged seven birdies and an eagle while another major winner, Bryson DeChambeau, is well-poised at 11 under.
Lucas Herbert was the biggest Australian mover on Friday, shooting seven-under 65.
Herbert's eagle and six birdies took him to eight under as compatriot and overnight co-leader Marc Leishman remained six under after an even-par round.
Leishman faltered with two bogeys in his initial five holes as the Australian contingent seek the first local win of an individual LIV title in Adelaide.
Cameron Smith is five under after firing a promising 67 and 23-year-old Elvis Smylie, who won on his LIV tour debut last weekend in Saudi Arabia, is three under.
Herbert and Smith achieved inroads as Kiwi Campbell, who turned pro in 2012 and has two Asian tour wins and an NZ PGA title on his resume, blitzed the sandbelt course in Adelaide's beachside western suburbs.
Campbell reeled off five consecutive birdies - and seven in 10 holes - plus his highlight-reel eagle. He and Rahm were one stroke shy of the course record.
American Talor Gooch shot successive 62s when winning the inaugural LIV event in Adelaide in 2023.
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