Bohn had played only the back nine when darkness fell last night and he completed a round of 67, with two birdies and a bogey in his front nine, to match Horschel's halfway total of 13 under par.
Horschel was yet to take to the course on Saturday, having completed a superb 63 on Friday night.
Matt Bettencourt and Scott Stallings were one stroke back, Stallings completing an eight-under-par 64 which contained two eagles on Saturday.
Australian Steven Bowditch was joined on 11 under by home players Bud Cauley and Luke Guthrie, with JJ Killeen and Jason Gore a further shot back.
Jason Kokrak eagled the last to join the group at nine under, which included England's Gary Christian after a 68.
But while the world's leading players were otherwise engaged at the Open, former Masters champion Mike Weir was condemned to an early exit from this week's consolation tournament after missing the cut on five over.