McIlroy appeared to be struggling once again early on but ignited his round with five straight birdies on the back nine before closing for the clubhouse lead on a six-under-par 66.
Afterwards, McIlroy said he had copied the approach to Bay Hill previously adopted by Woods, who is currently recovering from surgery after his recent car crash.
“I’ve watched Tiger enough here over the years and the way he played this course was he played it very conservatively,” said the former world No1. “He took care of the par fives and that was usually enough to get the job done. So, sort of take a little bit of a leaf out of his book.”
McIlroy shares the lead with Canadian Corey Conners, with the big-hitting Bryson DeChambeau just a stroke further back.
British trio Lee Westwood, Matthew Fitzpatrick and Martin Laird also enjoyed strong starts to the tournament with respective rounds of 69.
But the day belonged to McIlroy, who won the Arnold Palmer Invitational back in 2018 and has not finished outside the top six at the event since 2016.
Of his round, which started at the 10th tee, he said: “Obviously, a 66 is a great way to start a tournament. But I feel like you don’t have to do anything special to shoot a good score here. You can be really conservative off the tees if you want.
“The first few holes were a little slow going and I made a really good birdie on 14, and that sort of got me, got the round going. The two twos on the back nine were great. Coming off last week where I struggled with the par threes, it was quite a turnaround.”
McIlroy’s playing partner, Tyrrell Hatton, who has been one of global golf’s form players over the past year, struggled to a round of 77 while another playing partner, Francesco Molinari, the winner at Bay Hill in 2019, shot a 78.