The Northern Irishman missed a four-foot par putt at the 17th hole and then horseshoed-out from three feet at the last for a six-under-par 65 at Club de Golf Chapultepec.
"Starting the day I would have taken 65, but I feel like I could have been a few more ahead," McIlroy told Golf Channel after posting a nine-under 133 total.
Americans Phil Mickelson (68) and Justin Thomas (66) and Englishman Ross Fisher (68) were equal second on seven-under, with world number one Dustin Johnson (66) among a trio one stroke further back.
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Four-times major champion McIlroy, 27, is playing just his second event of the year, after missing six weeks due to a rib injury.
"I tried to approach this week, not with low expectations, but just to see how it went," said the former world number one. "My body feels good, which is the most important thing I think."
On a day when the holes seemed to have magnets, several players holed out from long range, none more spectacularly than McIlroy, whose approach at the 14th landed left of the green, but took a fortunate sideways bounce and trickled into the hole.
"I cut a little nine-iron in there, trying to take a bit of distance off it," he said. "It’s always a bonus to hole shots like that. It’s the second shot this year I’ve holed with that nine-iron so it’s been a good club for me."
Mickelson, meanwhile, had to call his brother Tim out of the gallery on the fourth hole when regular caddie Jim "Bones" Mackay was unable to continue due to a stomach illness.
But the 46-year-old Mickelson did not miss a beat, carding a 68 to stay near the lead.
Mickelson oozed praise about the course and the options it provided players.
"You can hit driver on every hole and with the altitude you can really try to overpower it," he said.
"However, the trees are so thick and dense you don’t have a recovery shot, so you have to hit the fairway. You can play aggressive on some holes and conservative on others based on how you feel."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Larry Fine)
