Niemann, who made 10 birdies and an eagle on Friday at the 54-hole event in Mexico, had four birdies and three bogeys Saturday to stand on 13-under 129 after 36 holes.
Niemann led by five when the day began but his margin was trimmed by a shot in round two.
Third-ranked Rahm, the reigning Masters champion playing in his first LIV event, fired a four-under 67 to match South African Dean Burmester in second on 133.
The Spaniard, who defected from the PGA Tour in December, started on the second hole in the shotgun start and made his lone bogey at the third before following with five birdies, two on par-5 holes and two more on par-3 holes.
Niemann's round is not the lowest in the history of the Saudi-backed upstart series as its third campaign begins. American Bryson DeChambeau carded a 58 to win last year's LIV Golf Greenbrier title in August.
Negotiations remain ongoing between the PGA Tour and DP World Tour with Saudi Arabia's Public Investment Fund to complete a framework agreement for a merger unveiled last June.
