The Chilean mixed seven birdies and two bogeys to tie Lee Westwood atop the leaderboard at 10-under-par 203 for the tournament, one stroke ahead of second-round leader Bryson DeChambeau and Richard Lee of Canada.
Niemann is bidding to become just the second player to successfully defend a LIV Golf title after Brooks Koepka in Jeddah.
Australia's Marc Leishman (71) stands alone in sixth place at six-under par while compatriot Cameron Smith is tied for 16th on three under after a battling 69.
Fifty-two-year-old Englishman Westwood made birdies on three of the final four holes to finish with a 68 at the Sentosa Golf Club, which played tougher than it did in the first two rounds.
"I would say it's a major championship-style golf course. It's very demanding," Westwood said.
"Even though the rough isn't that thick, it asks you to hit a lot of fairways, and it's difficult to score from the rough. You don't have as much control on the golf ball."
Niemann agreed about the challenge the course presents.
"I've been hitting the ball really good. I think that's the key," Niemann said.
"It's a really stressful golf course, I'll say. There's a lot of danger off the tee, a lot of water on second shots.
"One way or the other, I feel like I've been kind of like stress-free after I hit the shot. Once I get on the tee, there's some pressure there, and then once I hit the ball, it goes right where I'm seeing with my eyes, so it feels satisfying."
DeChambeau followed his second-round 65 with a one-over 72, but he wasn't dismayed despite bogeys at holes 8, 10 and 12.
"I played really well. The greens on 8, 9, 10, 11 got really slow," he said.
"For some reason, there wasn't as much wind around there and I guess the greens got slower in that area and I three-putted a few of them and that cost me some momentum. Other than that, I played great golf. I almost played just as good as yesterday, just things didn't line up."
Lee, a LIV Golf wild card, birdied the final hole to record a 69 and tie DeChambeau.
Spain's Jon Rahm shot an even-par 71 to stay within striking distance of the leaders, three strokes off the pace.
In the team competition, 4Aces are atop the leaderboard. Captain Dustin Johnson's round of 68 sent the team to 16-under, two shots ahead of Ripper GC and Legion XIII, and put Johnson in a tie for seventh place with six others at 5-under.
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