After finishing Round 1 at Colonial Country Club with five birdies in his final seven holes on Thursday, Woodland birdied two of his first four holes on Friday and added two more birdies at No. 9 and No. 11 to move to 9-under.
Lurking one shot back is local favourite Jordan Spieth, who had his own troubles mid-round before recovering for a five-under 65.
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. "But front nine I just got into a rut and played a bad run of holes, and obviously that put me out of the tournament". "It's pretty cool that the Tour is doing that, but when you're out there you're just so in the moment".
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"I'm still hitting it really well and putting it really well and those things go hand in hand", said the 29-year-old American, who is looking to claim his first PGA Tour victory.
He followed that up with a bogey on the par-3 16th and fell to 7-under for the tournament with two holes to play in the second round.
Jordan Spieth was far from ideal 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.
"That will be a bit odd", said Spieth. Once I got it back to even par I just wanted to given myself looks. "I'm sure tomorrow will feel pretty unusual, especially with so many guys in and around the lead".
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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.
Varner answered with eight birdies and wound up with a 66 for a one-shot lead over Spieth atop the leaderboard.
Players also have to undergo temperature screenings, regular COVID-19 testing and practice social distancing on tee boxes and in the clubhouse.
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