The Chilean stands at 14 under par 199 after his third-round 70, but his lead shrank from five strokes to two during the third round as Harold Varner III vaulted up the leaderboard with a 65 at Trump National Golf Club in Bedminster, New Jersey, on Saturday (local time).
England's Lee Westwood duplicated his Thursday round of two-under 69 to drop into solo third at 10 under par.
The team scores took a beating in the windy conditions. Niemann's Torque GC is the lone team under par at one under after amassing an eight-over score on Saturday.
Tom McKibbin's Legion XIII side lapped the field with a four-under round and closed to within two strokes.
Niemann, who played bogey-free golf through 36 holes while posting rounds of 64 and 65, opened with a double-bogey six after his drive on the 514-yard par-4 went out of bounds.
He shot 36 on the front nine after solving the outward half in 30 on Thursday and Friday.
Looking for his ninth LIV Golf individual title, Niemann steadied himself on the inward half. He made birdies at the 12th and 15th, but another wayward drive cost him an opportunity for birdie on the finishing hole, a 580-yard par 5.
Varner started the day tied for fourth, seven shots behind Niemann. He posted the lowest round of the day, making four birdies on the front nine.
Westwood admitted to some fatigue coming down the stretch on a blustery day. He was at 12 under through 12 holes, but took a double-bogey on No.14 and a bogey at 16.
"I'm just pleased to be in good enough shape, my game still at an elite level where I can compete with these guys that are some of the best in the world," Westwood said.
"At 53 years of age, I think it's quite an achievement to still be mixing it with the youngsters."
Niemann plans to carry a positive attitude into the final round.
"I mean, just be grateful," he said. "I feel like if I just remember the good things that I have around me and the people around me, it's just easy to go back to sleep. I have a good life."
Lucas Herbert is the leading Australian in the field, a distant 11 shots behind Niemann.
Herbert, who claimed victory at last month's LIV event in England, is three under after rounds of 66, 71 and 73.
Compatriots Marc Leishman and Travis Smyth are in a tie for 23rd at two over, while Cam Smith is six over.
- with AAP
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