Watney came from four back to beat defending champion Bo Van Pelt and Robert Garrigus by one on 22 under par, with Tiger Woods joint fourth after a 63, his second lowest round of the year.
A last-hole birdie would have given Watney a 59, but he bogeyed it the day after Van Pelt dropped two shots there when in the same position.
"I wasn't really thinking about winning, but the round sort of built momentum and things just kept getting better and better.
"After the first round I thought I was out of it to be honest." He was lying joint 38th in a 48-strong field.
The 31-year-old then had to wait to see if he could be caught, but Van Pelt failed to grab the birdie he needed to force a play-off.
Woods was only two behind after six birdies in his first 10 holes, but by the time he picked up more shots at the 16th and 17th Watney had moved clear.
"I left a couple out there," he said.
"I hit a bunch of good shots, but just had one little bad stretch yesterday. Other than that, I really played well."