Woods overcame windy conditions at Sherwood Country Club to finish 54 holes at 11-under-par 205.
He is seeking his sixth win at the event and his first since 2011.
Zach Johnson held onto second place with at 9-under with a 72 of his own.
Bubba Watson used a 3-under 69 to climb into third place at 7-under 209.
Matt Kuchar, meanwhile, fell to fourth with a third-round 4-over 76.
Webb Simpson grabbed solo possession one shot further back with a 69.