Keegan Bradley is a further shot back, while Justin Thomas looks unlikely to win the tournament for a third successive year as the FedEx Cup victor is 10 shots adrift of Perez following a one-under 71.
After finishing second and fifth here the past two seasons, and playing in the same group with the leader, Pat Perez of the United States, Matsuyama appeared to turn the corner with his eagle on the par-5 No. 3.
Perez fired a seven-under par round of 65 despite delays for bad weather.
Perez, whose last victory came at the OHL Classic at Mayakoba 11 months ago, made eight birdies following his first dropped shot of the week at the 12th after starting on the back nine.
His only blemish came on the par four 12th, his third hole of the day, where he had a five but back-to-back birdies followed on the next two holes to get his round back in credit.
Smith, who won his first US PGA Tour title at the Zurich Classic team event in May, picked up five shots on the way out and three more over the last five holes to stand a shot clear of Thai Poom Saksansin and Americans Xander Schauffele and Keegan Bradley.
With last year's victor, Justin Thomas, totaling 23-under par, Matsuyama believes he has his work cut out for him over the final two days.