Stenson, 41, outweighed three bogeys with four birdies for a round of 1-under 71 to push himself out in front on 12-under and one stroke ahead of playing partner Bryson DeChambeau, who posted a 72.
He made a 15-foot birdie putt on the 13th to take the lead over hard-luck Henrik Stenson, and then rolled one in from 20 feet on the next hole. On the third hole, he dropped in a sidewinding 38-foot birdie putt to negate the previous hole's bogey.
"Northern Irishman McIlroy, who holed an eagle, four birdies and a bogey on Saturday, added: "... golf is different than a football game, and there's etiquette involved, and you don't want people to be put off from bringing their kids when people are shouting stuff out.
ORLANDO, Fla. - Rory McIlroy wondered Saturday if limiting alcohol sales might help curb some of the loud and abusive behavior he believes is getting worse at PGA Tour tournaments. He had a one-shot lead with four holes to play in 2015 when he had consecutive three-putts - one for bogey, another for par - and Matt Every beat him with an 18-foot birdie on the last hole.
After a tense afternoon at Bay Hill Golf Club, McIlroy had looked poised for an uneventful finish when he stepped onto the 18th tee with a three shot lead. "It's not great to see him make putts because he was making them against me".
For the second Sunday in a row, Tiger Woods is back in the spotlight with a late final round tee time.
"I felt like I left one or two out there coming in and I definitely could have wrapped up a two or three-shot lead for tomorrow which would have been a nice cushion, but it didn't happen", he said.
Woods has had multiple surgeries in the past five years and his last victory came at the 2013 World Golf Championships-Bridgestone Invitational.
"Just because I won here eight times doesn't mean I'm going to win this week automatically", Woods said.
Englishman Rose (67) and American Ryan Moore (69) were a stroke back on nine-under. He fell no more than two shots behind, closing the margin when Stenson bogeyed the 17th.
"It feels good to be able to finally understand and feel that I can get into a round again". He has a chance to change that, which is all he wanted.
"I kept saying the last few weeks, I wasn't that far away and it just takes something to click into place", McIlroy said in a greenside interview.
At least he knows the course, even if he hasn't been here in five years.
"A lot of people are excited about how Tiger's starting to show signs in the right direction, and I think it's going to be a lot of fun over the next two days", Day said.