The American world number one ground out a level-par 72 in strengthening winds with several tough pin positions at Sherwood Country Club to end the third round of the tournament which he hosts with an 11-under total of 205.
In glorious late afternoon sunshine after a damp start to the day, Woods rolled in a 12-foot birdie putt at the par-four last to retain control of an event he has won a record five times.
"It was a tough day," Woods told reporters after offsetting four birdies with four bogeys. "The wind was all over the place. It was really tough to pull clubs and he greens were softer
"They were still pretty quick, and unless you got (the ball) above the hole, there are some really difficult pins out there.
"So it made it even more imperative to miss the ball in the right spots (below the hole), because we weren't going to always hit the ball tight. Obviously a lot of guys shot some higher numbers."
Compatriot Zach Johnson, the first-round leader, was alone in second place after also carding a 72 with 2012 Masters champion Bubba Watson a further two strokes back at seven under, after a 69.
Only four players in the elite field of 18 dipped under par for the day, Northern Ireland's Rory McIlroy the best of them with a six-birdie 68 that left him a distant 13 shots off the pace.
Woods, two shots in front overnight after equalling his own course record with a stunning second-round 62, made a confident start on Saturday, two-putted for birdie at the par-five second to maintain that advantage.
However he bogeyed the fourth, after taking a penalty drop when his tee shot ended up in a hazard, and the par-three eighth, after missing the green to the left off the tee, to drop back into a tie for the lead with Johnson.
Johnson briefly moved ahead after sinking a six-foot putt to birdie the par-four ninth but Woods immediately responded, draining a 12-footer for birdie at the 10th to get back to 11 under.
Just two holes later, Woods was handed a three-stroke advantage as Johnson, who had bogeyed the par-five 11th after hitting into trees, found a plugged lie in a greenside bunker at the par-three 12th on the way to a double.
Woods surprisingly three-putted from only five feet to bogey the par-five 13th, then three-putted from long range for a bogey at the short 15th as his lead was cut to one shot.
However, Woods recovered with a two-putt birdie at the par-five 16th, narrowly missing his eagle attempt from 15 feet, to forge two strokes clear.
Though Johnson rammed in an 18-foot birdie putt on the 18th green to get to nine under, Woods followed him with his 12-footer to retain a two-shot advantage.