The Australian star carded a steady two-under 68 third round with two birdies at Asiad Country Club in Busan on Saturday to be tied fourth.
Chile's prolific winner Niemann was a big mover as he posted six birdies and two bogeys in a 66 to catch second-round leader Gooch (71) at nine under.
Zimbabwe's Scott Vincent is one shot behind the leaders in solo third place after round of 67 with four birdies and a bogey, while Smith is tied with Charles Howell III (68).
Three golfers are lurking three shots off the pace, including Dustin Johnson after delivering Saturday's low round with a bogey-free 64. He is tied with New Zealand's Ben Campbell (66) and defending champion Bryson DeChambeau (71), whose eventful day included four bogeys and three birdies.
DeChambeau's Crushers GC sit atop the team standings at 16-under, one shot ahead of Gooch's OKGC and four up on Smith's all-Australian Ripper GC.
Marc Leishman is best placed of Smith's Ripper teammates, tied ninth at five under after a 68, with Lucas Herbert (69) one shot behind, while young gun Elvis Smylie is way back in tied 47th at four over after a 74.
Eight of the top-10 golfers on the leaderboard have won at least one LIV Golf title. Niemann holds the tour record with seven titles, including five in 2025, but is looking for his first of the season.
"Putter did behave a lot better today than the first two days, so pretty happy about that," Niemann said. "It did love me a lot. I did love it a lot, too."
Gooch, who has four LIV Golf wins, began his round with 14 consecutive pars.
"You've got to stay patient and just wait for your time and hope that it comes, and it unfortunately didn't come much today," Gooch said. "But that's why we stay patient. Maybe tomorrow it'll come."
This will be Gooch's 16th time playing in the final group at an LIV Golf event and the 14th time for Niemann.
Joining them in the last group is Vincent, who is filling in for HyFlyers GC captain Phil Mickelson and looking for his first LIV Golf title.
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