Na backed up his opening round 67 with a three-under par 69 to move to eight under 136, putting the one-time tour winner in front.
Current FedEx Cup champion Billy Horschel was pushing hard, making an eagle in the second hole and a birdie on the third to move to seven under after four holes.
South African Branden Grace (67) and Canadian David Hearn (71) are in the clubhouse at six under while Troy Merritt (six holes) and Ben Martin (five holes) are also six under.
“I wasn't very comfortable after I made the bogey on the first hole, but I made a nice birdie putt on two and followed right after on three,” Na said.
“My putter was definitely there today. I made a lot of good putts, key par saves, and some good birdie putts." But Na said he also hit a few loose ones because he felt a little tired.
"I didn't get enough rest because I got done so late yesterday and had to come out in the morning," he said.
“So I think the key is to get some good rest tonight and be ready tomorrow.”
Woods slammed home a nine-foot birdie on the ninth green, his final hole, to card a round of 71 and get him in at even par, right on the current cut line.
The 14-time major champion was loose at times as he battled his new swing, notching up five bogeys but countering with six birdies.
World number one Rory McIlroy parred his opening three holes to remain three under, five shots off the pace.
Phil Mickelson crashed with a 76, making a triple bogey on the 18th and a double on the sixth, to miss the cut.
“It's a tough course. I was thinking to myself as I was walking around, I can't believe I've actually won here,” the 2007 champion said.
“This is a very penalizing course. I kept hitting it in spots that were impossible recoveries.”
(Editing by Gene Cherry)
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