The American duo are a shot clear of Sergio Garcia and Billy Hurley III, who started the day top of the leaderboard, but Na will undoubtedly be happier with his performance.
Dropped shots at the sixth and 13th prevented Moore from taking the overall lead at the Kuala Lumpur Golf and Country Club, although he nevertheless put down a statement of intent with seven birdies to go 12 under overall for the only tournament sanctioned by the PGA Tour in south-east Asia,
Na's bogey-free round included five birdies, three in a row from the third hole, and he is quietly confident heading into the final day.
"It looks like I'm in a good position," he told the PGA's official website.
"I'm just going to go out there, play my game and stay patient."
Moore will be hoping the experience of winning the CIMB Classic in a play-off 12 months ago can give him the edge over Na and he certainly showed flashes of brilliance on Saturday, most notably with a long birdie putt on the 12th.
Garcia and Hurley III both remain in contention at the end of a third round disrupted by a lengthy rain delay.
A second successive 68 from Garcia started well with birdies on three of the opening five holes, but the Spaniard was unable to replicate that form after the turn.
Four players – including Gary Woodland thanks to an impressive round of 66 – are two shots behind Garcia and Hurley III, who was hampered by a pair of bogeys.