American Brendan Steele (67) and South Korean An Byeong-hun, who drained a 35-foot birdie putt at the par-four 18th to card a 66, shared the lead on 10-under 132.
"It was a good putt, perfect speed," An told Golf Channel about his sixth birdie of the day, and his third in the last four holes. "I hit it a bit harder than I wanted but it just caught the right lip and went in.
"I was hitting it well today," said the 25-year-old, whose best PGA Tour finish was a runner-up spot at the 2016 Zurich Classic of New Orleans. "Last week (at the Farmers Insurance Open) I was a bit shaky but Sunday I played really well, especially on the back nine.
"I was hitting some great shots, and now I have the confidence going." Matsuyama, who beat American Rickie Fowler in a playoff to win last year's Phoenix Open, recorded four birdies in his first 17 holes before bunkering his approach into 18, splashing out to six feet and narrowly missing the par putt. His first bogey of the tournament dropped him into a tie for third with Scotland's Martin Laird (66), American Matt Kuchar (69) and South Korea's Kang Sung-hoon (65).
"I played good, steady golf today," said overnight leader Kuchar, who had opened with a 64. "Two under doesn't keep up with yesterday's round but it's hard to keep up with a seven-under-par score."
World number six Jordan Spieth got to six under for the round after 13 holes but ran up a double-bogey at the 18th, after hitting his tee shot into water, to card a 68.
"Eighteen was rough," said Spieth, who ended the day at four-under, level with fellow American Phil Mickelson (70).
"We (he and caddie Michael Greller) discussed and I had Michael's confidence that if you hit it solid, for sure, it's going to carry that water.
"I smashed it and it still didn't carry, so that was a kind of a bugaboo on our part."
(Reporting by Mark Lamport-Stokes in St. Augustine, Florida; Editing by Andrew Both)
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