While Fleetwood enjoyed serene progress on Friday, McIlroy was 10 shots adrift after mixing two birdies with three bogeys over the first 12 holes.
But the world number two picked up four shots in his last six holes to post his second successive 69 and join Ryder Cup team-mate Viktor Hovland on six under.
“I felt like my approach play was pretty scrappy, missed an iron shot right on four, so that’s not ideal,” said McIlroy, who shook hands with Indian cricket legend Sachin Tendulkar after finishing his round.
“Being a little tidier and keep the bogeys off the scorecard, I think I can have a good weekend and get closer to the leaders.”
US Ryder Cup player Ben Griffin – playing with McIlroy and Hovland – recovered from a slow start to card his second straight 68 and sit four shots off Fleetwood.
Japan’s Keita Nakajima is 10 under after following a 65 with a 69, while Shubhankar Sharma is the leading Indian player on four under after a bogey-free 66.