American John Huh, who had eight birdies and one bogey, leads Appleby and Argentine Miguel Angel Carballo, who made two eagles, by one point.
"The format here you've got to make birdies," Appleby said. "You've got to think about six birdies a day. I had eight today. Probably could have had more but I made some putts of length."
Appleby has nine victories on tour, the most recent in 2010 at the Greenbrier Classic in West Virginia, where he carded 59 in the final round.
The 46-year-old, however, has struggled since, undergoing major back surgery in 2015.
The Barracuda Championship format encourages attacking golf by awarding eight points for albatross, five for eagle and two for birdie, while deducting one point for bogey and three points for double-bogey or worse.
(Reporting by Andrew Both in Cary, North Carolina)
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