Na, frequently taking excessive practice strokes and often backing away from his shot, otherwise struck the ball sweetly in carding a bogey free 68 to reach 12-under for the tournament.
The South Korean-born American met with rules official Mark Russell after his round to discuss his slow play but said there were no problems.
"We were talking about the pace of play. We were on the clock quite a bit. Everything's okay," said Na who blamed his problems due to a lack of comfort with his balance.
"As ugly as it is and as painful as it is, believe me, it is really tough for me and I am trying," he said.
Fellow American Kuchar had a mixed day, combining seven birdies with four bogeys, including one on the notoriously difficult 'island green' 17th, for a round of 69 to finish a shot behind Na.
"I knew it was going to be a tricky day, there were going to be a lot of bogeys and dangers around every corner," said Kuchar, who tied for third at last month's Masters.
"It was a great day in terms of not letting the bad holes bother me. I think that is one of my strong suits and today it came in really helpful."
Kuchar and Na began the day in a three-way tie for the lead with Zach Johnson, the 2007 Masters champion. Johnson shot a one-over 73 to slip back into equal fourth with Ben Curtis (70) at seven-under.
It was a sign of the difficulty of the course that Na and Kuchar were the only players to post three rounds in the 60s and Na was one of only three players, along with Curtis and Carl Pettersson, that were bogey free on Saturday.
While Kuchar and Na jostled for the outright lead, most of the buzz around a sun-drenched TPC Sawgrass layout surrounded Fowler.
The 23-year-old Californian, who claimed his first US Tour win at Quail Hollow last week, racked up seven birdies before spoiling his otherwise flawless round with a bogey at the last, missing a putt from less than four feet.
He ended the day perfectly poised, two shots behind Fowler and one behind Kuchar.
For most of the round, Fowler, who would become the tournament's youngest winner, was right on target, and even when he got in trouble, he remained unflustered.
On the fifth hole, he drove into a bunker, 200 yards from the pin, but blasted out of the sand to just four feet and made birdie.
"I drove it well, put myself in position off the tee, which is the key here, no matter what, especially with the wind blowing today. I was able to play out of the short grass as much as possible," said Fowler.
"Other than bogeying the last, I'd have to say it was a fairly perfect round."
Tiger Woods made an even-par 72 and was two-under for the tournament, tied for 34th place. Phil Mickelson signed for a 69 to climb 16 places to be equal 14th.
Spain's Sergio Garcia made a double bogey on the par-five second hole to tumble back to a tie for last place but recovered to finish with a four-under 68 leaving him level with Mickelson.