Woods used a strong finish, including an eagle with a 20-foot putt at the 16th, and took advantage of a struggling Justin Rose to wrest control of the leaderboard as the round came to an end.
He finished the day at 11-under 205, two strokes ahead of Rose, who bogeyed three of his last six holes to card an even-par 72.
Rickie Fowler (67) and John Huh (71) shared second place with Rose at 9-under.
Woods will be seeking his eighth career win at the event. Only Sam Snead has won a single tournament that many times -- he took the Greater Greensboro Open in 1938, 1946, 1949, 1950, 1955, 1956, 1960 and 1965.
Should he hang on for the win, Woods will be world No. 1 for the first time since late 2010.
Second round co-leader Bill Haas stumbled to a 1-over 73, falling into a tie for fifth with Thorbjorn Olesen (66), Gonzalo Fernandez-Castano (68), Jimmy Walker (70) and Ken Duke (70) at at 8-under 208.