Both golfers collected five birdies. Cink logged his seventh career first-round lead while Henry was on top after 18 holes for the fifth time.
Defending champion Adam Scott, the runner-up at last week's Masters, ended the day in a five-way tie for second place at minus-4, notching five birdies and a bogey.
Also in the group were Jhonattan Vegas, Vaughn Taylor, Charley Hoffman and Kevin Chappell.
One shot further behind at 3-under 69 were Geoff Ogilvy, Brandt Snedeker, Jim Herman, Kevin Streelman, Brendan Steele and Troy Matteson.
Also making news Thursday was Kevin Na, but for the wrong reason. He carded a 16 on the par-4 ninth hole -- the worst score on a par-4 since the PGA started keeping hole-by-hole records in 1983.
Na's misadventure is also tied for the second-worst score on any hole since then.