Following his press conference, McIlroy, who finished 18-under for the tournament and three shots ahead of Bryson DeChambeau, made sure to toast Arnie with his signature Ketel One vodka.
Stenson, whose only victory since his lone major title came previous year at Greensboro, began on the back nine and saved pars from seven feet at the par-five 16th and 15 feet at the par-three 17th after finding bunkers off the tee.
Another 10-foot birdie at the ninth left McIlroy on 13-under with Stenson after the Swede made bogey at eight, missing the green on his approach and botching a six-foot par putt to set up the back-nine battle.
"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.
"The last time I won a PGA Tour event was the day Mr. Palmer passed away and so it's a little bit ironic I come here and win".
Both players missed the 10th green on their way to bogey-fives, allowing Fowler to move into a three-way tie for the top by following a front-nine 34 with three birdies in a four-hole stretch.
After going more than two years without winning on the PGA Tour while trying to patch his personal life back together, Woods finally broke through at Bay Hill with a five-shot victory over Graeme McDowell. I thought I really putted well this week. "Brad's one of the best putters to play on the PGA Tour, so it was great to be able to pick his brain for a couple hours".
Stenson began the day in a share of the lead and claimed the outright advantage with a 12-foot gain at the first, only for playing partner DeChambeau to drain a 20-footer at the par-three next.
Woods shot a 3-under 69 to get to 7 under in the tournament, certainly within striking distance back in his prime. He's first got to take care of his part of that equation and the number is probably something in 64 to 66 range. He has a chance to change that, which is all he wanted. "I'll hopefully be within two or three of the lead, and I can make a run at it". "I knew if that could translate from practice onto the course, I could have a good week".
"Over the weekend past year I was hitting driver pretty much everywhere, leaving myself wedges in".