The Northern Irishman shot his lowest score since 2019 to take second place heading into the final round.
After starting the day nine shots off the lead, McIlroy ended it in second place after a second straight bogey-free round, highlighted by five successive birdies from holes three to seven and a spectacular finish in making a 21-foot eagle putt on the last.
McIlroy’s lowest round since 2019 left him at 19-under par, two behind Fowler, who was in similarly strong form with five front nine birdies and four more coming home in a blemish-free 63.
On a leaderboard flush with UK players, Tyrrell Hatton was four shots off the lead in equal-sixth after a 67, with fellow Englishman Ian Poulter a further stroke away after also shooting five-under.
England’s Paul Casey was eight off the pace at 13-under after a 70, a shot ahead of Tommy Fleetwood who had four birdies on each nine in a bogey-free 64.
Sharing third place at 18-under were Australian Adam Scott (67), America’s Robert Streb (65) and Mexico’s Abraham Ancer (63).
McIlroy, the former world number one who has this year dropped to 14th, later said he could not remember his last bogey-free round before this tournament, where he suddenly has two.
“I think on a course like this you’re going to have stretches where you’re going to play good golf and hit good shots and maybe just not hole the putts," a-t-il déclaré aux journalistes.
“I played an eight-hole stretch yesterday in even par — I made eight pars in a row. Then today, I played nine holes in 6 under and all of a sudden you feel a little better about yourself.”