Starting on the 10th hole, McIlroy made 11 straight pars, which included a three-putt par on the par-5 18th.
Fleetwood, the defending Abu Dhabi champion and last year’s European Tour money-list winner, continued his excellent form by hitting all 18 greens in regulation.
There was a five-way tie for third place with Fabrizio Zanotti, Ross Fisher, Thomas Pieters, Bernd Wiesberger and Sam Brazel shooting 67s.
Top-ranked Dustin Johnson drove his ball into a lake at the ninth, his closing hole, to finish with a 72. Matt Kuchar was also on level-par while Justin Rose went one better with a 71.
McIlroy, who hit 17 greens in regulation, collected his first birdie of the day by making an uphill 15-foot putt at the third and made further birdies at the seventh and eighth.
“First competitive round in over 100 days so it’s a little bit different,” said McIlroy, who last played at the Dunhill Links Championship in Scotland on Oct. 8. “But I did well. I stayed patient.
“I gave myself loads of chances. Really pleased. I played very solid. I think I only missed one or two greens, drove the ball well and the iron play was pretty good. So just need to keep doing that over the next three days and I should have a chance.”
Fleetwood said he had control of his ball throughout.
“It was very good . very stress-free,” he said. “Played really well from start to finish.
“Felt like I did what you need to do well around this golf course, which is drive it well, hit your irons, but you can’t really be too greedy all the time. My pace putting was really good. (Hitting) 18 greens doesn’t happen very often so nice to do it around here.”