The 28-year-old, whose most recent triumph came on the day that Palmer died in September 2016, finished on 18-under at Bay Hill - three in front of Bryson DeChambeau.
Four-time Major winner McIlroy started the day with five pars, before three birdies across the next four holes to put him on the way to victory.
Speaking to Sky Sports News after ending his trophy drought, McIlroy said: "I played a perfect round of golf. It was awesome to feel the buzz of being somewhere around the lead going into the back nine.
"I've missed it, I really have missed it, and to play the sort of golf that I played today under that pressure, I'm really proud of myself and just so happy to win."
McIlroy returns to action at the World Golf Championship Match Play in Texas later this week.