Holding the overnight lead with Justin Rose, Varner hit a wild opening drive at the tenth on his way to a triple-bogey seven and was still over-par for his round until holing a 30-footer at the fourth.
Justin Thomas (66) and U.S. Open champion Gary Woodland - who got into the mix with birdies on his last two holes for a 66 - are also one shot behind.
While Rose was unable to keep pace, Varner - seeking his maiden PGA Tour title - used a flawless front nine to remain the player to beat heading into the third round.
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.
"Although my game wasn't great the first couple of holes, I made a few putts, I knocked one in from just off the green on my first hole of the day, looked at my caddy and said, "Welcome back".
After a bogey at 18, Varner closed with a flourish that started with a 31-foot birdie putt at the par-three fourth.
US unemployment rate drops in May as economy reopens
Employment in May was boosted by restaurants and bars, which added 1.4 million jobs after losing 6 million in April and March. Small businesses, however, have been continuing to take a big hit over the past month, despite the BLS's rosier jobs report.
"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 said. But once you get into it, it's the same. "I remember when I won Hilton Head and played well in the majors, the crowd started getting behind you and you start feeling like you can't do anything wrong".
Spieth passed a big test, with another to come as he tries to end almost three years without a victory.
Sitting one shot back in the first PGA Tour event following a three-month COVID-19 break was a pack of five golfers that included world number four Justin Thomas (66), three-times major victor Jordan Spieth (68) and reigning U.S. Open champion Gary Woodland (66). He punched it low into a back bunker and saved par.
Gary Woodland, left, and Justin Rose, of England, almost touch fists on the 18th green following the third round of the Charles Schwab Challenge golf tournament at the Colonial Country Club in Fort Worth, Texas, Saturday, June 13, 2020.
Third round play begins at 8 a.m. EDT Saturday in Fort Worth.
Rory McIlroy reacts during the Charles Schwab Challenge in Fort Worth, Texas, on Friday.