Isenhour, who set the 18 and 36-hole records for this tournament by himself, shares the new 54-hole mark with Pappas. Their total of 200 bettered the old record of 202, which Vance Veazey set last year.
Parker McLachlin struggled to a 1-over 71 and stands alone in third place at 7-under-par 203. Tim O'Neal had the round of the day, as he matched Isenhour's course record of 63 at Panama Golf Club.
That moved O'Neal to 6-under-par 204. He is tied in fourth place by Joe Daley (66) and Kevin Gessino-Kraft (69).
Isenhour opened with a two-shot lead, but that dipped to one as he bogeyed the second. Pappas, playing one group ahead of Isenhour, birdied the third to move to minus-8.
The 37-year-old Isenhour stretched his lead back to two shots with a birdie on the fourth. Pappas quickly got the margin back to one with a birdie at No. 5. Isenhour then bogeyed the fifth to slide to minus-9.
Pappas birdied the sixth to climb to 10 under and the lead. The South African parred his next five holes before draining his next birdie at the 12th.
The 35-year-old birdied the 14th to get to minus-12, three clear of the field. Pappas, who is looking for his first tour win, stumbled to a bogey on 15 and three-putted for bogey on 18 to drop back to 10 under.
'I played beautifully and kept it in play between the trees and that's always a goal of mine,' Pappas said. 'I never really was under pressure. My ball striking has been solid and I like the fact that I'm very relaxed.'
Isenhour, meanwhile, parred nine straight holes from the sixth. He picked up just the second birdie of his round on the par-4 15th. He parred out to share the overnight lead.
'Today, I just didn't hit the shots the way I've been doing the first two days,' said Isenhour, who is a two-time winner on the Nationwide Tour. 'I hit some really good ones, but I also hit some really bad ones. My wedges were awful. I had a few easy ones and I failed to convert every one of them.'
Kyle Thompson posted a 3-under 67 to climb into a tie for seventh at 5-under-par 205. He was joined there by Kevin Durkin, David Hearn, Scott Petersen, Travis Perkins and Mario Tiziani.
Garrett Willis and Jason Allred each carded 66s to move to minus-4. They share 13th with Craig Kanada, Paul Claxton and Matt Hendrix.