The Australian's dead-accurate, 11-foot putt on the 18th hole easily found the cup to complete his history-making round of 11-under-par 59, and he celebrated 30 minutes later in the clubhouse as Jeff Overton's attempt to overtake him at 22-under 258 fell one stroke short.
Appleby's 59 was the second in 25 days on the PGA Tour. Paul Goydos shot the fourth 59 in history July 8 during in the first round of the John Deere Classic.
Overton's try at a 4-foot birdie putt on the 17th lipped out and he could only manage a par on the final hole, finishing alone in second place at 21-under 259.
Brendan de Jonge (65) claimed sole possession of third place at minus-17.
Fourth place went to Woody Austin (63), Paul Stankowski (64) and Roger Tambellini (65), all of whom finished at minus-15.