He moved his way in to contention with two birdies in his fist six holes as the three overnight leaders quickly dropped shots in the tougher conditions, tying the lead with Schauffele at the eighth before moving in to sole possesion on the ninth. "Obviously conscious that it could have gone either way, but I knew I was going to do my best".
"It's wonderful to stand here with the Claret Jug", Molinari told reporters after a closing 69 secured an eight-under tally of 276 and a two-stroke victory over Rory McIlroy, Justin Rose, Kevin Kisner and Xander Schauffele.
"It's insane. Absolutely crazy to think so many people can follow a person", he said.
Woods played his "one bad swing" at the 18th, but lady luck intervened to keep his ball out of Barry Burn and in thick rough that at least gave him a shot.
Feeding off the electrifying atmosphere, Woods sent a laser-guided second shot to the 10th that left him a tap-in birdie, then at the 11th he rolled a 95-foot eagle putt to five feet and tapped home to gain another shot.
"My record around here was awful, which didn't make me too optimistic about the week", he said.
But while a year ago Spieth survived a wobble in the final round at Royal Birkdale to take the title, this time he was too erratic, not recovering from a bogey at the fifth that was followed by a double-bogey at the long sixth where his second shot found a gorse bush.
The 42-year-old American legend - beset by personal problems and back issues for most of the last decade after once dominating the sport - threatened a shock victory at Carnoustie when, halfway through his final round, he led while most of his rivals were shedding shots. "I had a chance starting that back nine to do something, and I didn't do it".
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He has also made comments in the press that his daughter looks "terrified" by her new position as Prince Harry's wife. I want my friends to marry princes. " People will think you're whining - being a royal comes with privilege".
Woods stirred this remote Scottish town on a balmy afternoon, his name going to the top of the competitors in the 147th Open when he two-putted the 14th green for a birdie.
Adam Scott and Jason Day will wonder what might have been after Australia's British Open title drought extended to 25 years with another unsuccessful tilt at Carnoustie.
"I didn't play very well on the front". It was still a fantastic tournament for Woods, who entered today with a chance to contend and managed to do just that, coming slightly unraveled on the back after a double at 11 and a bogey at 12 knocked him from the lead.
Molinari finished at 8-under 276, the lowest score in eight Opens at Carnoustie, the course where Jean Van de Velde threw away the British Open with a triple bogey on the last hole in 1999, where Padraig Harrington twice hit into Barry Burn on the last hole to make double bogey and still won.
He quickly set aside his anger and produced a sublime approach shot onto the green - Molinari congratulating him as the passed - taking the applause of the crowd with a wave of his cap.
McIlroy, Rose, Schauffele and Kisner finished in a tie for second place as the world's oldest major championship avoided a fourth straight playoff at Carnoustie to determine the Champion Golfer of the Year.
"Playing with Tiger makes it even more special". (I was) just happy to claw my way back a little bit. Williams is one of the few athletes on the planet with whom Woods can relate - an aging, larger-than-life superstar who is fiercely competitive and adept at overcoming adversity.