He posted a 10-under 203 total, one shot ahead of fellow American Patrick Cantlay (69), who curled a 55-foot birdie putt into the middle of the hole at the par-four 18th.
Four others are two behind -- Americans Kevin Na and Tony Finau, Australian Cameron Smith and halfway leader Graeme McDowell.
Watson, whose wife was a professional basketballer, played in the NBA All-Star weekend celebrity game in Los Angeles on Friday.
Back at home on grass instead of hardwood, he started his third round in style with a tap-in eagle at the par-five first, but acknowledged it was a tough slog the rest of the way.
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"It was a grind full time," said the 39-year-old, who won at Riviera in 2014 and 2016. "It was easy when you have a tap in. Then I just hung on the rest of the time."
Watson has slipped to 117th in the world rankings after an ill-fated experiment in 2017 with a different brand of ball.
He has not exactly set the world on fire in three previous starts this year but hopes to stay on an emotional even keel in the final round.
"You've got to know that this golf course is going to make you mess up, the grass, the way the ball bounces on it, you're going to have shots you think are perfect and ended up not perfect," he said.
"But it's golf, not just this week but every week. You're going to know you're going to make a mistake, especially on a Sunday, and you've got to keep fighting and hopefully your fight is better than everybody else's fight."
(Reporting by Andrew Both in Adelaide, South Australia; Editing by Greg Stutchbury)
