Rahm is holding a two-shot lead from a chasing pack featuring Herbert in Sunday's final round at the Grange.
Rahm and US star Bryson DeChambeau teed off as co-leaders at 19 under.
But the American has faltered with four bogeys in six holes, including spraying a tee shot at the par three 3rd into a catering area.
DeChambeau has slipped to 15 under, overtaken by local hope Herbert and American Anthony Kim, both at 17 under.
Herbert carded four birdies in a mid-round hot streak as he seeks to become the first Australian to win an individual LIV title in Adelaide.
Cam Smith is 15 under and one under for his round, while Englishman Tyrell Hatton (16 under) and Colombian Sebastian Munoz (14 under) remain in touch.Â
But the steely Rahm (20 under) - except for a bogey at the eighth - has showed little signs of letting his lead slip, though has failed to make a clean break on his rivals.
Smith's all Australian Ripper GC of Herbert, Elvis Smylie (eight under) and Marc Leishman (13 under) hold a one-stroke lead for the team title from Rahm's Legion XIII.
The 23-year-old Smylie, who won the individual title on his LIV debut last weekend in Saudi Arabia, gained momentum with four birdies in a six-hole stretch but then missed a three-footer for par on his seventh hole.