The 22-year-old Englishman seeks his first career US PGA victory after three European Tour triumphs, the most recent last November at Dubai when he captured the World Tour Championship by one shot over compatriot Tyrrell Hatton.
"I played nicely all day," Fitzpatrick said. "Didn't really hit too many loose shots. I just kept it fairly steady and managed to hole a few putts too."
England's Paul Casey shared third, one stroke off the pace, with former US Open winner Lucas Glover and fellow American Charley Hoffman while Australians Greg Chalmers and Ryan Ruffels were in sixth on 69.
Fitzpatrick, who began his tour of the famed Orlando layout on the back nine, birdied the par-5 16th after reaching the green in two and added back-to-back birdies at 18, sinking a 15-foot putt, and one, dropping a 25-footer.
He birdied the third after dropping his approach three feet from the cup and added another at the par-5 sixth, blasting his third shot from a greenside bunker to four feet and sinking the putt.
Grillo endured a wilder ride with birdies at the third and par-5 fourth holes, then closed the front nine with birdies on four of the final five holes -- three putts between eight and 13 feet and the last a 47-foot birdie effort at the ninth.
The South American standout, whose lone US PGA win came at the 2015 Frys.com Open, followed with birdies at the 11th, par-5 16th and par-3 17th. He missed a 19-foot eagle putt at 16 for a tap-in birdie before dropping a 40-foot birdie bomb at the penultimate hole.
Grillo was left reflecting on what might have been a lower score, saying he had struggled to get to grips with chilly early morning temperatures at the start of his round.
"It was very tough, it was very cold this morning," Grillo said. "I couldn't feel my fingers on the first five or six holes. I made a couple of mistakes on the first few holes.
"So it might have been an even better round -- but I'm really happy with my play overall."
Aussie Jason Day, the world number two, was in a 12-man pack on 70 that also included South Africans Louis Oosthuizen and Trevor Immelman, Canadians Adam Hadwin and David Hearn, Sweden's Alex Noren and Aussie Aaron Baddeley.
Day said later he was still struggling to rediscover his best form.
"I just don?t quite have enough confidence in my swing right now," Day said.
"I feel like my putting's right there, but it's still lacking. It's kind of all the parts of my game right now are just behind a little bit."
Japan's Hideki Matsuyama, ranked fourth, opened on 73 while third-ranked Rory McIlroy, hoping for a fifth career major title and the completion of a career Grand Slam at next month's Masters, fired a 74.