Varner fired a four-under-par 66 at Colonial Country Club to reach 11-under 129 after 36 holes in the US PGA Tour's return event after a three-month shutdown due to the coronavirus pandemic.
Harold Varner III chats with Jordan Spieth after finishing their third round of the Charles Schwab Challenge golf tournament at the Colonial Country Club in Fort Worth, Texas, Saturday, June 13, 2020.
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.
"Those are ones where you just have a ton of them when you're playing in competition but you're picking them up a lot of times when you're playing regular rounds of golf at home".
But, maybe excessively positive, Spieth ran his birdie putt 3 feet past the hole. "At the moment, it's just you and your caddie out there".
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"It was a nice, positive start to the day and therefore I was able to get the momentum going on my front nine, which was the back nine, and actually played much better golf as the round went on and felt like I had opportunities to get in a little bit lower than I did".
Spieth, a three-time major champion, recovered with birdies at five and six to limit the damage and keep alive hopes of ending a three-year winless drought. This moved Bradley to even-par for the round.
"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.
"I played a really, really solid round of golf with a 20-minute hiccup for a couple holes", he said.
Rose birdied the last to sign for a level-par 70 to join Justin Thomas and US Open victor Gary Woodland in the group four strokes back, with Brooks Koepka - who played alongside McIlroy - on four under after a second successive 68.
Birdies at two, six and seven put McIlroy at eight-under and one off the tournament record with two to play but his chances of 61 ended with a bogey as he joined Xander Schauffele (66) and Collin Morikawa (67) at nine-under.