Piercy covered the back nine in two-under 34 to remain on track for his third PGA Tour victory but will have to contend with a Sunday shoot-out as 15 players head into the final round no more than four shots off the pace.
Overnight leaders Kim Meen-whee of South Korea and Australian Mark Hensby carded 68s in the third round to slip back into a tie for third at 12 under with Americans Jason Gore (63) and Will Wilcox (65), and Argentina's Emiliano Grillo (67).
While Piercy was delighted to share the lead with Barnes after 54 holes, he was also "a little frustrated" after struggling on the greens.
"I shot six under today and I missed it from two feet on 15 and I had a whole bunch more that were realistically birdie putts," the 36-year-old told reporters.
"I still made some, but as often as I'm hitting it close, I feel like I should be making a few more.
"I've been striking it well. I'm hitting it where I'm looking, right distance control. I just need to get that putter a little bit dialled in a little bit more."
Barnes, still hunting his first win on the PGA Tour after coming closest with a tie for second at the 2009 U.S. Open, enjoyed playing with Piercy in the third round as the two golfers effectively spurred each other on.
"We both got off to a great start, we both holed about a 20-footer on the first hole," said Barnes. "So we saw balls going in the hole, saw good shots ... it's not so much competing but kind of feeding off each other."
Barnes made a timely surge up the leaderboard with four birdies in the last eight holes on Saturday.
"I had a good back nine," said the 34-year-old. "I've been playing well all week, been putting the ball in good position.
"This is a course where you need to be in the fairway to score just because with the bermuda rough, it's tough to control your distances ... I've managed that pretty well the first three rounds."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry/Peter Rutherford)
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