Sweden’s Stenson, the 2016 British Open winner, dropped his approach inside four feet from the cup at the par-5 12th hole to set up a bogey that left him one-under for the third round and 12-under overall at Bay Hill.
American Bryson DeChambeau was one stroke back in second after 12 holes with compatriot Rickie Fowler third at 10-under after 14 holes.
England’s Justin Rose held the clubhouse lead at nine-under 207 after a third-round 67.
Woods, a 14-time major winner, again showed solid form with the Masters looming in three weeks, firing a three-under par 69 to stand on 209 through 54 holes at the Orlando layout where he has captured eight career titles.
“I figure I’m within reach if I shoot a really, really low round tomorrow,” Woods said. “I’m going to have to shoot a low one and get a little bit of help. But my responsibility is to go out and shoot a low one first.”
Woods curled in a 12-foot birdie putt at the par-4 18th to complete his day, cocking for a full-speed fist pump before adopting a mellow low-key finish because “I figured that would probably (only) get me within five or six of the lead.”
Woods found a greenside bunker at the par-3 second hole and missed a 10-foot par putt but answered the bogey with birdies on three of the next four holes.
After curving in a 38-foot putt at the third, Woods sank a five-foot birdie putt at the par-5 fourth and, after a par save from a greenside bunker at five, sank a 15-foot putt at the sixth.
Woods took another bogey at the par-4 eighth, finding the right rough off the tee and missing a 10-foot par putt, only to answer it by making a 10-foot birdie putt at the par-4 11th.
Woods went birdie-bogey at 16 and 17, escaping a bunker at the par-5 16th but missing a 15-foot eagle putt then finding a greenside bunker at the par-3 17th and missing a 17-footer for par.
“Never give in to the golf course (or) certain shots,” Woods said. “Just trying to make the best possible score and dig it out on every hole. I made three bogeys but I made three birdies right after that so that’s positive.”