The 14-time major champion was collecting birdies in droves early in his third round at the Quicken Loans National, and by the time Woods reached the seventh hole on a steamy Saturday, he was within a stroke of the lead at the tournament he's hosted since 2007.
He finished at 21-under 259, while American Ryan Armour shot 68 for second place on 13-under. Kelly led after the first three rounds, but he finished the tournament without making a putt longer than 12 feet.
A spectacular chip-in and four putts beyond 15 feet were among his seven birdies, the 14-time Major victor sharing 11th on five-under 135 after 36 holes at TPC Potomac course, only four strokes behind United States co-leaders Brian Gay, Beau Hossler and Ryan Armour. His shot was even more impressive given only one other birdie was made on the hole during the final round.
It's the 10th career European Tour victory for the 35-year-old Swede, who started the day seven shots behind compatriot and 54-hole leader Marcus Kinhult.
He shot a two-under 68 in his third round on Saturday.
Tiger Woods shot 66 and tied for fourth, his best finish in three months, though he never got closer than four shots. Even though he missed a few short putts on the front nine, he closed with a 30-foot birdie putt on the par-3 17th and hit wedge into 5 feet for birdie at the 18th. Horschel carded a 68 to stay one stroke off the lead, tied for fourth with Molinari, who came in with his own 65 in the second round. In 1999, he shot 294 and finished T7.
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Woods' final-round performance featured six birdies, bogeys on the 11th and 13th holes, and a gutsy 16-foot par putt on the closing hole.
The 14th is a drivable par-4, and Woods hit the green both days, only to see the ball bound over. Teryn Schaefer presents the best social media posts from around the world of golf in "Good, Bad & Unusual" and after each day's play brings you the biggest talking points in "The Takeaway".
"Really proud of what I've done", Molinari told CBS Sports.
"I missed some putts this week, but that's okay as long as I'm starting the ball on my lines again and I have the speed", he said. "I played great on the back nine, the start was incredible". Woods is particularly satisfied with his putting after making the switch to a TaylorMade Ardmore model before the tournament.
Tiger Woods smiles as he walks on the 16th fairway during the final round of the Quicken Loans National golf tournament, Sunday, July 1, 2018, in Potomac, Md. That's something I've been missing for a while now, for the better part of nearly two months.
Woods moved up 15 spots to No. 67 in the world, meaning he might need at least a top-10 finish at the British Open to crack the top 50 and be eligible for the Bridgestone Invitational, which is being held for the final time at Firestone, a course where Woods has won eight times. You can get away with eight bogeys and a double at the Quicken Loans National because it's the Quicken Loans National.