Thompson's 62 was one stroke of Gavin Coles course record that was set last year on the North Course at Crestview Country Club.
Ryan Hietala and Jamie Broce share second place at 7-under-par 64. Ten players share fourth at minus-6.
Thompson, who won the New Zealand PGA Championship earlier this season, started on the back nine and quickly moved into red figures.
He birdied the 11th and came right back with a birdie on 12. Thompson collected his third birdie at the par-5 14th.
Thompson also birdied the 15th and 16th, to cap a run of five birdies in a six-hole span. He turned in minus-6 as he birdied the par-5 18th.
The 26 year old birdied the par-5 second, giving him birdies on all three par 5s. Thompson made it two straight as he also birdied the third.
Thompson settled down as he parred the next three holes. He collected his final birdie on the par-4 seventh.
'I drove it long and straight today. That's a good combination, especially on this golf course,' stated Thompson, who is fifth on the money list. 'I had wedge in my hand a lot today.'
Hietala birdied three in a row from the 12th and turned in minus-4 after a birdie at the 18th. The 33 year old birdied the first and fourth before a bogey on six. He holed out for eagle at the par-4 ninth to share second.
'I saw it land, but I couldn't see what happened after that,' said Hietala. 'I got up to the green and couldn't see the ball. They told me it was in the hole, so that was fun. It was a nice way to finish the day.'
Broce ran off three birdies in a four-hole span from the 11th. After he bogeyed the 16th, Broce eagled the par-5 18th to make the turn at four- under.
The 30-year-old Broce birdied three of four holes from the second, but tripped to a bogey on the sixth. He recovered that lost stroke with a birdie on the eighth before a par at the ninth left him tied for second.
Martin Laird, who won earlier this year at the Athens Regional Foundation Classic, leads the group in fourth at 6-under-par 65. He was joined there by Jason Enloe, David McKenzie, Chris Anderson, Tommy Tolles, Mark Walker, Troy Kelly, Greg Chalmers, Mike Sposa and Brad Elder.
Legend Financial Group Classic winner Jason Day heads a group of 11 players one stroke further back at minus-5.