Watney birdied the final three holes and five of the last six on the par-71 TPC Summlerin layout en route to a 54-hole total of 17-under 196.
"I'm trying to keep it really simple," Watney said of his approach to the event, which is officially called the Justin Timberlake Shriners Hospitals for Children Open and which opens the US tour's post-playoffs Fall Series.
"I've driven the ball pretty well and it's just been fairly easy to hit quite a bit of greens. I think that's what you need to do out here is give yourself as many chances as possible. I've been able to do that so far.
"This course is right out there in front of you," added Watney, who won the WGC-Cadillac Championship at Doral in March and the AT&T National in July. "It's fairly short for Tour standards, so it's just about execution."
Na, who shared the overnight lead with Venezuelan rookie Jhonattan Vegas and South Korea's Charlie Wi, carded a five-under 66.
He had five birdies and a bogey in his outward run, and got to 17-under with his only birdie on the back nine, at the par-five 16th.
"I got off to a really good start on the front nine, made five birdies," Na said. "I felt like I could go real low with a bunch of birdie holes on the back.
"Unfortunately, I slowed down a bit and missed a few short ones. But to finish five-under for the day, I was pretty pleased."
Robert Garrigus carded a 63 and Kris Blanks a 66 to lie a stroke back on 197.
Garrigus, who had been hospitalized in Phoenix last Monday for dehydration, launched his round with four successive birdies and birdied three of the last four. He finished with a total of nine birdies and just one bogey.
"I started off on fire," Garrigus said. "It was just one of those days when everything was going in early, and I knew if I could sprinkle in some (birdies) late it would be a really good day, and it ended up being nice.
It was a further stroke back for Tommy Gainey (64), Paul Goydos (66) and Tim Herron (67).
Vegas, who had a share of the lead after each of the first two rounds, carded a 69 to join a group on 199 that also included Sweden's Carl Pettersson (66).
Watney, Na share lead at Justin Timberlake event
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