Byrd shot a 5-under-par 67 at the Quail Hollow Country Club for a three-day total of 15-under 201.
Byrd won the final event on the PGA Tour in 2010 and the first one in 2011, but since then has missed the cut four times in 10 tournaments.
He began his run of birdies by reaching the fringe of the green in two at the par-5 10th and two-putting from 30 feet. Byrd then made birdie putts of 3 feet at the 11th, 9 feet at the 13th and 6 feet at the 14th before hitting the green in two at the par-5 15th and two-putting.
Andres Romero, Kevin Na and first-round leader Bill Haas shared fifth place at 205. Phil Mickelson struggled to a 74 and was eight shots back in a tie for 16th.
Swim Week Miami Beach 2014 [PHOTOS]