Moore, who won the title last year after a Monday playoff against Gary Woodland, mixed seven birdies with two bogies, for a total of 12-under 204 in the $7 million tournament, co-sanctioned by the PGA and Asian Tour.
Korean-born Na, a former Asian Tour Rookie of the Year, joined him at the top of the leaderboard with five birdies.
World number four Sergio Garcia, the highest-ranked player in the field, fired a 68 to share third spot with overnight leader Billy Hurley III (71), a stroke behind the leaders.
With three more Americans, including Woodland, and South Korea’s Bae Sang-moon, a three-time Asian Tour winner and double PGA Tour champion, lying fifth at nine-under 207, Moore knows he faces another close finish on Sunday.
“I’ve just been able to play good, solid, consistent golf so far, just putting it on the fairway, giving myself chances and I’ve been fortunate enough to make some putts,” the 31-year-old Moore said. “So in the end that’s why I’m here.
“You know, I’ve been here, I’ve done it on this course, and so that should just give me that little extra going into tomorrow.
“I know what it’s like to win out here and I’m going to try and make that happen again.”
Na, 31, won his maiden professional title with the Asian Tour in Malaysia in 2002 and with Saturday’s only bogey-free card in the field he has a chance to win his second PGA title.
“It’s always nice to play bogey free, and I thought if I shot 67, somewhere around in there, I’d be very close to the lead,” Na said, recalling his last Malaysia win as a teenager.
“I remember my dad was caddying… I was just a kid, made the turn and looked at the leaderboard and I was like, man, I looked at my dad and I was like, I’ve got a chance to win this tournament, and birdied 10, 11, 12 and 13 and had a two-shot lead.
“It wasn’t the easiest last two holes coming in but I hung in there. I remember it like it was yesterday.”
Former world number one Lee Westwood started brightly with three birdies from his first five holes but five bogeys saw him sign for a 74 to stand tied 18th, seven shots off the lead.
(Writing by Sudipto Ganguly; Editing by Ken Ferris)