Appleby's 11-under round put him at 22 under, giving him a one-stroke victory to end a four-year winless drought. Third-round leader Jeff Overton (67) narrowly missed a long birdie try on the par-3 18th that would have forced a playoff.
Appleby is the fifth PGA Tour player to shoot 59. The Australian's round came less than a month after Paul Goydos had a 59 at the John Deere Classic. The others to shoot 59 were Al Geiberger (1977 Memphis Classic), Chip Beck (1991 Las Vegas Invitational) and David Duval (1999 Bob Hope Classic). Appleby's 59 was the first on a par-70 course. Goydos' came on a par 71 and the others on par 72s.
Appleby, 39, had nine birdies and an eagle in his round on the Old White course, including birdies on the final three holes with putts of under 15 feet.
"You don't shoot a low number . . . feeling a huge amount of indecision," Appleby said. "I was just comfortable."
Appleby saw playing partner D.A. Points flirt with a 59 on Saturday before settling for a 61. Sunday, it was Appleby's turn. "It was nice to be on the receiving end," said Appleby, who won for the first time since the 2006 Houston Open.
Appleby trailed Overton by seven strokes to start his round and was playing three groups ahead.
Appleby shot 6-under 28 on the front nine and eagled the par-5 12th before settling for three straight pars. He got his momentum going again with birdies of 15, 10 and 11 feet on the final three holes.
Overton had 34 putts in the final round, three-putting three times.
"I got beat by a 59," said Overton, who had his third runner-up finish of the year and remains winless in five years on the Tour. "What can you say? I played great, hit a lot of great shots. You can't win golf tournaments when you putt it that bad."