Molinari left with his first PGA Tour victory, unleashing a shot-making clinic on the field en route to a final-round, course-record-tying 62 on Sunday to win the Quicken Loans National at TPC Potomac at Avenel Farms in Potomac, Md., in the northwest suburbs of the nation's capital.
Molinari eagled the par 5 10th - rolling in a 49-foot putt after finding the green in two - and birdied the 11th, the toughest hole at TPC Potomac, to build his lead to six strokes.
Though he came up short, the quality of Woods' iron play for most of the week suggests he is getting closer to adding to his 79 PGA Tour victories and ending a five-year winless drought.
He was also quick to credit host Tiger Woods, who ended up in a tie for 4th place with Abraham Ancer at 11-under-par, 10 shots behind Molinari.
Armour closed with a 68 to finish second, earning one of four spots to the British Open. In a familiar scene that's played out on the weekends in three previous starts, especially on Sundays, Woods put himself onto the front page of the leaderboard only to start making silly and, at times, shocking mistakes.
Following his fourth round at the Quicken Loans National, which doubled as his final tune-up for the Open, Woods was asked his thoughts on the upcoming championship at Carnoustie.
Woods opened with a bogey, finding deep rough on his first two shots, then rescued par from bunkers at the second and third, praising his new mallet putter. I don't know. But somebody ranked No. 6 (!) on the PGA Tour in strokes gained tee to green is not going to be held out of the winner's circle.
When co-leader Ancer opened with a bogey, finding sand with his first two shots, Molinari took the lead for good. "Evidently I would have to shoot 24 on the back nine".
Woods, whose 79 career US PGA victories are three shy of Sam Snead's all-time record, has not won a title since the 2013 WGC Bridgestone Invitational - a drought of 1,791 days in which 114 different rivals have taken victories.
I don't love Tiger's chances at the Open if only because of the glut of talent at the top tier of golf. "Last year I think I missed the Tour Championship by one shot, so that's the mission this year, and this is a good step forward".
"I came here obviously because I was right on the bubble in the FedEx Cup and I wanted to gain a better position, so I guess job done", he said.
"Overall it was a good solid day", Woods said.
The top 15 remained the same, with Brooks Koepka holding the top spot, followed by Dustin Johnson, Patrick Reed, Justin Thomas, Bubba Watson, Jordan Spieth, Rickie Fowler and Bryson DeChambeau for the eight automatic spots on the team.
"I've never played a major", the 42-year-old Armour said. "I thought that 10 under would have been a good score for me to end up at for the day, and I could have easily gotten that today on the back nine".
"Francesco was phenomenal", Woods said.
Molinari signed with Bettinardi at the start of the year and has worked closely with famed putter maker Robert Bettinardi to create the best model for his game.