Bohn's total bested the previous record by one shot. That mark was set back in 1982 by Calvin Peete.
John Rollins and J.P. Hayes also posted Sunday 66s to share second place with Brendan Jones (68) and Ryan Palmer (67) at 23-under-par 265.
Bohn rolled in his first birdie putt on the par-4 second at En-Joie Golf Club. He parred his next five holes. Bohn birdie the par-5 eighth to get to 20 under.
The 32-year-old came right back with a birdie on the ninth. Around the turn, Bohn took advantage of the par-5 12th where he picked up the fourth birdie of his round.
Bohn moved into a tie for the lead at minus-23 with a birdie on the 16th. He birdied the par-3 17th to move one shot clear of the field. Bohn sank a short par putt at the last to close out a bogey-free round.
Jones, who led entering the round, could have forced a playoff with an eagle at the par-4 closing hole. However, he only managed to birdie the hole to share second.
Michael Allen and Ben Crane each posted rounds of 8-under 64. They shared sixth place at 22-under-par 266 with Mathias Gronberg, who closed with a 66.
Harrison Frazar posted the round of the week with his 10-under 62 on Sunday. He moved into the lead at the end of his round, but the leaders were early in their rounds at that point. His minus-20 score was good enough to tie for ninth place with Arjun Atwal, Jay Delsing and two-time champion Joey Sindelar.