That had catapulted him right into contention, but after going out in front on his own midway through Sunday, he promptly dropped three strokes in two holes at the 11th and 12th.
Molinari, 35, certainly earned his Claret Jug, playing nearly flawless golf on a gusty day off the eastern Scottish coast.
Francesco Molinari, Woods' partner on Sunday, won the tournament with no bogeys over the final 37 holes.
"To play the weekend bogey-free, it's unthinkable, to be honest". They were together three weeks ago when Molinari closed with a 62 to win the Quicken Loans National, with Woods presenting him the trophy.
"Even though he's won 14, you have to learn how to get back".
"This was his first taste of major championship drama for quite a while", McIlroy said. His grin grew very big as he said, "Oh, yeah".
"A little ticked off at myself, for sure", Woods said. That would stem from Nos. Another bogey on the next hole, and he was basically out of the tournament. At the long par-three 16th his tee-shot just failed to stay on the green and he three-putted. "I knew I was coming in with some good golf but my record around here was awful".
His anger over his mistakes was tempered by perspective, comparing it to Serena Williams losing in the finals at Wimbledon.
'Man, I just didn't make a putt today. I know that they know how much this championship means to me, and how much it feels good to be back playing again.
In a freakish moment on the 18th tee, a fan screamed right in the middle of Woods's backswing, but his drive still found the first cut on the right side. Yet he parred in from there, whereupon the four-time major victor said, "It was great, just to be a part of it and hear the roars. It was cool. It was really cool".
He regained some form in 2018, most crucially gaining regular play time without any injury concerns, and now at Carnoustie, Tiger Woods is the betting favourite to win his 15th Major.
"For the first time I felt I was ready for it". I've already gone through the frustration. When you put yourself in position enough times, it goes your way sometimes and it doesn't sometimes.
Schauffele had to settle for second place with Rory McIlroy, Justin Rose and Kevin Kisner, all of whom had plenty of reason to hope on a warm, windy afternoon that put plenty of bite back into Carnoustie.
The name "Woods" atop the board? "I remember having a shower and brushing my teeth so I'd say I was fine".
"That putt on the last, I'll never forget", he said.
Kisner, in a three-way tie for the lead with Spieth and Schauffele, took double bogey on No. 2.
We're getting a look at vintage Tiger stuff today.
"I've made a lot of progress over the year that's been kind of an off year, a building year", said Spieth, who came third at the Masters in April but then missed the cut at the US Open.
Molinari also admitted he tends not to contest the Dunhill Links Championship in the autumn as he has been "beaten up" on the links at Carnoustie a few times.