Even with major champions Stenson, McIlroy and Justin Rose starting the day ahead of him, Woods made it feel like he was about to turn the board (and possibly the golf world) upside down with just three weeks to go before Masters Sunday.
Woods played in the afternoon and went through the front nine with no birdies and two bogeys, dropping him nine shots behind.
Two years ago, he was tied for the lead with five holes to play until two bogeys over the next three holes.
The four-time major victor chipped in for a birdie at the par-4 15th hole to extend his cushion to two shots atop the leaderboard at the famed Bay Hill course.
"I'll tell you after Augusta!" he said with a grin.
"Just because I won here eight times doesn't mean I'm going to win this week automatically", Woods said. I'm just playing shots, playing the holes, playing angles, where to miss the golf ball, all these things are becoming more intuitive. "For a long time when I did kind of get out here a little bit, he was never here and it was a sore disappointment to have him not be here".
Rory McIlroy has always been one of the most honest and thoughtful voices in the sport, so he had plenty to say when asked if he had any incidents with unruly fans at Bay Hill.More news: Russia warns against 'anti-Russian hysteria' in Israel
Stenson, the 2016 British Open champion, fired a one-under 71 to stand on 12-under 204 after 54 holes, as American Bryson DeChambeau shot 72 to be one stroke adrift. "I didn't drop a shot, where I could have easily dropped three shots on those holes". "I can't really ask for much more".
Woods begins the final round five shots back of Stenson after a 3-under 69 Saturday.
"It's tiring", said McIlroy, who previously felt Tiger Woods may have missed the cut at last month's Genesis Open partly due to the added strain of having to persist with extra attention from fans at the course. And on the final hole, a 12-foot birdie putt was punctuated by an enthusiastic fist pump to end his day.
McIlroy shot a five-under 67 Saturday to vault to third at 10 under. "I got it up-and-down when I needed to, I took advantage of some of the good shots I hit", said McIlroy, who ranks second in the field in strokes gained/putting, a stat he ranked 124th in entering the week.
"Today was a hard fight, it was a grind", he said.
In trademark fashion, 14-time major victor Woods refused to rule himself out of the contest as he chases a ninth victory at Bay Hill. He at least managed to birdie the par 5s on the back, and had a tough par save on the 15th. "And if it gets warm like it's supposed to get on the weekend, then we're going to make some birdies".