The 23-year-old American, who began the day two shots back of overnight leader Dustin Johnson, shot a bogey-free six-under-par 64 to reach 13 under for the tournament.
Woods had last played in February at Riviera and the back issues come with the year's first major in a Covid-19 shuffled schedule coming on August 6-9 at the PGA Championship at Harding Park in San Francisco.
Tiger Woods and Peyton Manning held off a late challenge to beat Phil Mickelson and Tom Brady 1Up in a charity golf match in Florida on Sunday that raised $20 million for Covid-19 relief efforts.
The coronavirus relief golf match featuring Tiger Woods, Phil Mickelson, and Super Bowl-winning quarterbacks Tom Brady and Peyton Manning will be held on May 24 at Medalist Golf Club in Hobe Sound, Florida.
US golfer Phil Mickleson gave a positive response to a tweet asking whether he can play a round of golf with Tiger Woods in isolation with a cameraman on livestream
As well as being up against a highly motivated and well prepared International team, the US players faced a steep learning curve to become familiar with a Royal Melbourne course most had never stepped foot on until Tuesday morning.
Tiger Woods will be the first playing captain in the Presidents Cup since American Hale Irwin in its inaugural edition in 1994.
Making the most of good scoring conditions in the morning, Coetzee started with two birdies and picked up three more shots from the sixth hole to surge ahead as he reached the turn in 31.
The 20-year-old Japanese rank outsider, who earned her nickname because of her radiant smile, rammed home a lengthy birdie putt of just under 20 feet at the final hole to edge out American Lizette Salas by one stroke.
Donald Trump and John Bolton are on different tracks when it comes to foreign policy, and that is particularly problematic when the US is beating the drums of war.
Despite two bogeys in the final three holes, a one-under-par 70 was enough to clinch the title on a day when most of the contenders struggled at Country Club of Charleston.
US President Donald Trump met with Japan's Emperor Akihito who took the Chrysanthemum Throne only three weeks ago, after his father stepped down in the first abdication in two centuries.
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