Cink finished 54 holes at 15-under 195, two shots better than second-place Heath Slocum, who turned in a 64 on Saturday.
Kevin Streelman, a first-round leader last week at the U.S. Open, had a 62 in round three and is tied for third place with Vijay Singh (64), Tommy Armour III (65), Kenny Perry (65) and defending champion Hunter Mahan (67) at 12-under 198.
Of the top-14 players on the leader board, Mahan's 67 was the worst score by two strokes.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys