McIlroy posted six birdies and an eagle throughout a formidable second-round show in Texas, along with his sole blemish approaching his remaining gap, leaving the Northern Irishman simply two behind Harold Varner III at the highest of the leaderboard.
After an opening 63 to match Britain's late-starting Rose for the first-day lead, Varner took a seven at the par-four 10th hole to begin his second round, soaring off the tee and finding a bunker and rough before reaching the green.
"If you going to make a triple do it while you are playing well", said Varner, who is seeking his first win on the PGA Tour.
Not only was McIlroy unable to mount a charge but he also finished the week four shots back of South African namesake Rory Sabbatini, who shot a bogey-free, five-under-par 65 to finish the Charles Schwab Challenge in a share of 14th place.
The PGA Tour is back underway without fans at Colonial Country Club amid the coronavirus pandemic, which suspended the season in March.
"When you have spectators and things, you get on a roll, and most of the time you feed off of that", said Branden Grace, whose third consecutive 66 left him one shot behind. "You know, I like to feed off the crowds".
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"You can do as much practice as you want and play as much as you want at home, but until you actually get into that competitive environment, you're never 100 per cent sure of how your game is", McIlroy mentioned.
Jordan Spieth was far from flawless in the third round at Colonial on Saturday but the three-times major champion said it was a measure of his recent progress that he was still in the hunt for his first title in three years.
Spieth has struggled for form - his last tournament victory came in 2017. He then made back-to-back birdies on the front nine to move to 11-under par.
"I did a really good job of staying very neutral where I'd been kind of getting really negative or down on myself in the past", he told reporters. Three putts from 50 feet away gave him a triple bogey to start his second round after ending in a first-place tie with Justin Rose on Thursday.
Xander Schauffele chips to the 16th green during the third round of the Charles Schwab Challenge golf tournament at the Colonial Country Club in Fort Worth, Texas, Saturday, June 13, 2020.