The 36-year-old American fired nine birdies in all, including four on the last five holes, the final one coming on 18 after a 139-yard second shot that bounced into the flagstick and stopped four inches beyond the cup.
"It was about playing steady," Watson said.
"It was about being consistent. It was about hitting the driver somewhat in play, hitting the wedges somewhat close and then making the putts and that's what I did."
It would be his second title of the 2014-15 season, having won the World Golf Championships HSBC Champions event in China last November.
Watson matched the low round of his career to grab the advantage with fellow Americans Keegan Bradley, Harris English, Jason Gore and Brian Stuard plus South Korean Noh Seung-Yul sharing second on 64.
Birdies at the third, par-5 sixth, seven and ninth holes left Watson four-under at the turn. He birdied the 12th, 14th and 15th before taking his lone bogey at 16, but answered by closing with his third set of back-to-back birdies of the day.
Watson took advantage of benign conditions compared to last week's difficult terrain at the US Open at Chambers Bay, where Jordan Spieth added his second major title after collecting the Masters green jacket in April.
"Coming off last week, you can score around here, you can hit some good shots," Watson said.
"You still have to play golf but it's more relaxed and you still feel like you can score around here.
