A stroke in front overnight, the American left-hander twice fell two off the pace as first Adam Scott and then Jason Kokrak broke clear but he regained control of the tournament with two birdies in the last three holes.
Watson, who has always loved playing on the iconic Riviera Country Club layout, shot 68 on a breezy afternoon to land his ninth PGA Tour title with a 15-under total of 269.
"It means a lot," Watson, who won the 2014 Northern Trust Open two months before claiming his second Masters title, told CBS Sports in a greenside interview.
"You never know when your last (win) is going to be. So for me to come back and to win, and pull one out in a tough way, is special for me and my family.
"It's all about staying patient with (caddie) Teddy (Scott) in my ear. It's been a struggle over the last five years but it's going in the right direction."
Australian Scott, after an electrifying start that included an eagle and three birdies in his first six holes, carded a roller-coaster 67 to share second place with long-hitting American Kokrak (68).
"There wasn't a lot in it," said Scott, who ended his round with a birdie-birdie flourish, including a chip-in at the last.
"I played a good round of golf around a pretty demanding course again today."
World number three Rory McIlroy squandered a fast start with an erratic putting display as he shot 75 to finish nine shots off the pace.
A final-round shootout was always on the cards and the day began explosively as playing companions Scott and McIlroy both sank lengthy putts to eagle the par-five first, Scott sinking a 36-footer and McIlroy a 24-footer.
By the time Watson lined up a three-foot birdie at the same hole, five players were level with him at the top of the leaderboard, at 12 under.
Though Watson briefly regained his one-shot advantage with his birdie at the first, he was soon overtaken by the red-hot Scott, who drained putts from 32 feet at the third, 20 feet at the fourth and four feet at the sixth to move two strokes clear.
Scott stumbled with a double-bogey at the eighth, after his tee shot ended up in a creek bed dividing the two fairways on the hole, as the leaderboard bunched up again before Kokrak moved two ahead with a four-foot birdie putt at the 13th.
However Kokrak also faltered, with a bogey at the 15th after he over-hit the green with an adrenalin-fuelled approach, and Watson took control for good with birdies at the 16th and 17th.
(Editing by Andrew Both)
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