World number 735 Romero, whose last win on the European Tour came at the BMW International Open two years ago while he was ranked 837th, backed up his second-round 61 by recovering from a poor start to round three to reach 14-under for the tournament.
"I really feel good this week, I have a lot of friends around, I like the golf course very much," he said. "I hope that tomorrow I will play on the same level that I did today."
McIlroy was one shot off the lead held by Malaysian Gavin Green overnight, but the four-time major winner could only manage a one-under 69 and is now 11-under overall.
"I don't know what happened," said the four-time major champion.
"Felt a little flat out there, a little tired. Maybe it just all caught up with me. Looking forward to getting to bed early and getting a good night's sleep."
The 38-year-old Romero will play with Wade Ormsby in the final group, after the Australian's third-round 67.
Romero was three-over for his round after a double-bogey on the fourth hole, but a scintillating four-hole stretch that saw him card three birdies and an eagle secured the lead, with the help of Ormsby's closing bogey.
Green also started slowly before an eagle at 14 kept him in contention at 12-under, level with world number 13 Tommy Fleetwood.
Popular Englishman Fleetwood, bidding for his first title of the year, rolled in four birdies in his last seven holes to sign for a 68.
McIlroy, fresh of his PGA Tour Championship victory and $15 million (13.6m euros) FedEx Cup triumph last weekend in Atlanta, looked set to end the day in the mountains challenging for the lead.
But three bogeys in the final five holes, including one on the short par-five 14th, proved costly.
"I would love to win here, I just didn't quite have it today in the way that I did the previous days, especially yesterday," added McIlroy.
"I need to gather myself, get rested up and put everything I have into tomorrow."
The world number two is still one of a host of players who will be confident of making a Sunday charge, though, including former Masters winner Sergio Garcia who sits at 10-under.