Bohn led by three after consecutive Stefani bogeys at holes 16 and 17 at the El Camaleon in Playa del Carmen, Mexico.
But the two-time PGA Tour winner's lead stands at just one stroke as Stefani bounced back to birdie 18 while Bohn dropped a shot to close the gap.
Both Bohn (four-under-par 67) and Stefani (68) shot 66-65 in their first two rounds, with the leading pair at 15- and 14-under-par respectively.
Tied for third are American Charley Hoffman (67) and German Alex Cejka (68), three shots from the leader at 12 under.
Hoffman strung together four straight birdies on his front nine, while Cejka's five birdies for the day were marred by a double-bogey on the par-three 10th.
New Zealand's Danny Lee (67) is among four players in a tie for fifth at 11 under, alongside Americans Andres Gonzales (66), Jerry Kelly (67) and Ken Duke (70).
Fred Funk (69) is outright ninth on 10 under, while Mexican Oscar Fraustro (69) and American Nicholas Thompson (71) round out the top 10 on nine under.
Harris English (69) climbed 20 spots on the leaderboard to a tie for 26th at six under, but the defending champion is all but out of winning contention - sitting nine shots off the lead.
English is tied with 36-hole leader Michael Putnam (77), who was 13 shots worse off from Friday to Saturday as he blew his chances of breaking his PGA Tour duck.