The British Open champion rolled in seven birdies, including a 50-footer and a 35-footer in ideal morning conditions on the Innisbrook Resort's Copperhead Course at Palm Harbor.
One month before the year's first major, Stenson has already turned an eye towards Augusta National, where he has no top-10 finishes in 11 starts.
"This is one tournament of a few leading up to Augusta so we want to get some answers where the game’s at," the world number six told Golf Channel.
"I’m very happy with that, especially putting. Long game I can go the range and work on a little bit. I don’t think I’ve been playing super good any time going into Augusta, so I’m just working away.
"We’ve got some work to do but I’m not too worried about it."
Stenson, 40, finished second at the Dubai Desert Classic on the European Tour five weeks ago, before last week exiting the WGC-Mexico Championship during the first round due to a stomach bug.
He and all of the other leaders on Thursday played in the morning, enjoying calm conditions on a day when the afternoon starters averaged more than two strokes higher.
"The morning is the time for scoring around here," he said. "It’s certainly a good idea to be quick out of the blocks and we did that."
Stenson's 64 was matched by American Russell Henley, while leader Herman reeled off five birdies in his first seven holes en route to the lead.
"I was driving the ball really well, putting myself in position for good iron shots and I was putting really well. That all usually adds up to a pretty good score," said Herman.
The 39-year-old is a late bloomer who enjoyed a coming out party in 2016, winning the Houston Open.
A former club pro at Trump National Bedminster in New Jersey, he was a frequent golf partner of United States President Donald Trump.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Frank Pingue)
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