Playing his eighth full-time season on the PGA Tour, Barnes posted an 11-under total of 205 to end the round a stroke in front of his compatriot Brendan Steele, the 36-hole leader who slipped off the pace as he ground out a 72.
American Charley Hoffman, bidding for his fourth win on the U.S. circuit, carded an adventurous 70 on a sun-splashed afternoon to finish at nine-under, level with England's Luke Donald (68).
"A bad swing at the end," 2002 U.S. amateur champion Barnes, 35, told reporters about his wayward tee shot at the 18th. "If you told me five under today, I would have taken it before the round.
"This is why you play the game, right? Come in on Sundays and have a chance to win. Just need to keep what I'm doing the last three days."
Barnes, ranked 262nd in the world, has made 221 starts on the PGA Tour without winning, his best finish a tie for second at the 2009 U.S. Open where he led after 54 holes.
Steele, the 2011 champion, began the round with a three-shot advantage but that was quickly cut to one when he bogeyed the second, after hitting his tee shot into an unplayable lie in a cactus, and Barnes birdied the first and third.
Barnes joined Steele in a share of the lead when he sank an eight-footer at the sixth before Hoffman made it a three-way tie at the top with a birdie at the par-five eighth.
Though Barnes stumbled with a bogey at the ninth, he rebounded with birdies at the 11th, 12th, 14th and 17th, where he laid up with an iron off the tee and hit a wedge approach to six feet, to break clear of a tightly bunched leaderboard.
Barnes then paid the price for his errant tee shot at the last as he advanced his second from thick rough just 100 yards before running up a bogey six.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Andrew Both)
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