Woods, who came into the day leading by seven, never saw his advantage shrink to less than six strokes throughout Saturday's play on the South Course at Firestone Country Club, carding birdies on the first two holes to get off to a quick start.
He ended the day at 15-under-par 195 and will seek to close out his eighth win at the World Golf Championships event Sunday.
Ending 54 holes alone in second place at minus-8 was Henrik Stenson, who fired a third-round 67.
Jason Dufner claimed sole possession of third one shot further back with a 67 of his own.
Keegan Bradley, after challenging Woods early in the round, stumbled to a 1-over 71, ending in a seventh-place tie with Miguel Angel Jimenez (65) at 5-under 205.