Fitzpatrick carded a flawless 67 at Bay Hill to join Argentina's Emiliano Grillo at the top of the leaderboard, with compatriot Paul Casey a shot behind alongside Lucas Glover and Charley Hoffman.
In contrast, McIlroy's 74 included four bogeys and a double bogey, while Stenson - who has finished in the top 15 in his last five appearances in the event - double-bogeyed the 18th in a 75 matched by Blayne Barber.
The American was a last-minute replacement for Danny Willett after the Masters champion withdrew due to illness.
Fitzpatrick eclipsed Nick Faldo's record as the youngest Englishman to win three times on the European Tour with victory - and the first prize of more than £1million - in the DP World Tour Championship in November, two years to the day after gaining his card via the qualifying school.
The 22-year-old from Sheffield has taken advice from McIlroy on buying property in Florida as he plans to gain his PGA Tour card, a task which would be completed with a win at Bay Hill.
Starting from the 10th, Fitzpatrick followed six straight pars with birdies on the 16th and 18th to reach the turn in 34, before picking up further shots on the first, third and sixth.
Casey played the course the other way round and cancelled out two early birdies with a double bogey on the eighth, but birdied the 10th and then three of the last four holes to complete a 68.
Defending champion Jason Day was part of a large group on two under, with Olympic champion Justin Rose a shot further back.
This year's event is the first since tournament founder Palmer died in September at the age of 87 and numerous tributes are being made to the seven-time major winner.
A 14-foot bronze statue of Palmer was unveiled at the course on Saturday, while several players have the tournament's ''umbrella'' logo on their bags for the week.
Asked for his favourite memory of Palmer, Day told PGA Tour Live: "I think having the celebratory drink with him after the win last year. No one else gets to do that any more and it's sad, but that's something I will hold very special to my heart because I was the last to do it."
Palmer's grandson Sam Saunders had been placed in the same group as McIlroy for the first two rounds and matched the world number three's opening 74.
Saunders was two under par with five holes to play, but bogeyed the 14th and 16th and took six on the 18th after his approach finished in the rocks on the edge of a water hazard guarding the green.
In an interview broadcast on PGA Tour.com, Fitzpatrick said: "I played nicely all day, didn't hit too many loose shots and managed to hole a few putts as well, so when it all clicks it's nice.
"I learnt the hard way last year, I didn't hit many greens at all and I was getting up and down from everywhere and managed to still finish tied 27th, so something I had in mind this year was purely to hit more greens.
"In the long run I would love to play more over here as well as keeping my place in Europe but that's something to figure out hopefully if I can get my tour card over here."
McIlroy, who is making just his third start of the season due to a rib injury, told ESPN: "There were positives in there. I hit a few good shots, especially coming down the stretch.
"Even on the last I felt I hit two good shots; I caught a gust of wind with my second and it hit the rocks and ricocheted over to the bunker.
"I got a couple of good feelings there coming in so I'm going to work on them on the range and see if I can straighten it out for tomorrow."