Garrigus made a blazing start with three early birdies and opened up a four-stroke cushion at the turn at the Copperhead course in Palm Harbor.
He threatened to run away with the tournament but did not make a birdie on the back nine, ending his day on a sour note when he missed a five-foot putt to shoot one-under-par 70, leaving a group of players move within striking distance.
Garrigus stands on an eight-under 205 total, with Na (68) on seven-under.
Australian John Senden, a two-time runner-up at Innisbrook, compiled a brilliant bogey-free 64 to vault within two strokes of the lead, while Englishman Justin Rose (69) bogeyed the last and trails by three.
Garrigus, eyeing a second tour victory, also missed a short putt at the 12th hole but was upbeat after his round.
"This is the position you want," the 36-year-old told PGATour.com. "I haven't made a bad stroke yet except for those couple (of putts on the back nine) and I'm hitting it well, so I'm looking forward to tomorrow."
Garrigus and Na were "on the clock" for slow play for much of the back nine and each received a 'bad time' warning - Garrigus on the 13th hole and Na the 14th. A second 'bad time' would have resulted in a one-stroke penalty.
The fidgety Na never looked comfortable over the ball, but his bogey at the 10th was his first, and so far only, dropped shot this week.
"The back nine I felt a little rushed," said Na, who did not think he and Garrigus deserved to be on the clock, even though at times they were nearly two holes behind the pair in front.
"When I'm playing slow I'll be the first to admit it but I didn't think I was playing slow and Robert plays fast."
Senden, widely regarded as one of the world's top ball-strikers, looked the part as he ran off seven birdies.
"I've been doing some great work with my coach Ian Triggs and wanted to take it to the golf course," Senden said after sinking a 30-foot birdie bomb at the last.
He shared the low round of the day with Retief Goosen, a two-time U.S. Open champion whose world ranking has slipped to 318 after back surgery in 2012.
Goosen became frustrated when he could not convert his early birdie opportunities, but his drought turned into a deluge as he made three in a row from the seventh hole.
"Suddenly I made one and hallelujah, it started happening," said Goosen, who ended the day four shots off the pace.
"I made a 15-footer with a big break and from then on suddenly the hole was bigger."
(Reporting By Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)