Na, who along with Zach Johnson and Matt Kuchar held the advantage after 36 holes, recorded birdies on two of his last three holes to finish the day with a slight advantage over Kuchar at 12-under 204.
Na is looking for his second career PGA title.
Kuchar led most of Saturday at TPC Sawgrass but splashed his ball into the water in front of the island green at the 17th, ending with a bogey.
He finished the round with a 3-under 69, leaving him at minus-11.
Rickie Fowler, who triumphed last week at Quail Hollow, made the day's biggest move, firing a 6-under 66 to claim sole possession of third at 9-under 207.
Sharing fourth place were Johnson (73) and Ben Curtis (70).