Watson entered the final round in a sixth-place tie, four strokes behind overnight leader William McGirt, but reeled off five birdies on the first eight holes Sunday to get back into contention.
He carded six straight pars on the back nine and birdied No. 18 at Riviera Country Club to finish at 15-under-par 269, completing his first victory since the 2012 Masters.
Dustin Johnson registered a 5-under 66 to grab sole possession of second place at 13-under 271.
Sharing third one shot further back were Brian Harman (68) and Jason Allred (68).
Charl Schwartzel (68) took fifth at minus-11.
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