He was tied there with third round co-leader Kevin Kisner. I wish I could have taken the last four holes back, but it is what it is.
The sun was peeking out of the clouds and Woods was walking up the first fairway when one spectator, a beer in his hand, shouted: "Go on Tiger, we got your back".
Woods also birdied No. 14 - after playing a pitch shot from the back of the green that is shared with No. 4 - to move back to 5 under, two off Molinari.
Not since Padraig Harrington achieved the feat a decade ago has The Open produced a back-to-back victor.
Now he finds himself primed to follow up his victory at Royal Birkdale 12 months ago and become the first golfer to retain the British Open title since Padraig Harrington a decade ago.
"However, if the bad weather doesn't come in, then we know we're going to have to shoot eight under par on Sunday". He's re-grouped, though, and has the scent of victory in his nostrils again.
Jordan Spieth set the tone pulling driver on the 396-yard opening hole and sending it bouncing and rolling to 10 feet for eagle.
The American superstar joked with reporters at his press conference on Saturday after going under the clippers at Magic Barbers on Carnoustie High Street earlier that day. Birdies at the fourth, 11th, 14th and 16th in a bogey-free effort was a splendid day's work.
It took a chunk out of Dustin Johnson and Justin Thomas, the number one and two players in the world who won't be around for the weekend. "It was a dream start for the day".
"I've been a little too careful and tentative in these big tournaments", he added.
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Clear cut chances were few and far between in the opening 15 minutes, despite both sides playing at a good tempo early on. Obviously we can not say more about this now, but that's of course the most negative thing about the day.
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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.
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Spieth finally hit the front alone when he birdied the 16, but 2017 US PGA Tour Championship victor Schauffele and smooth-putting Kisner made their combination of great birdies and par saves late to keep pace.
The way golf has been going, it would be reasonable to see the name "Johnson" atop the leaderboard and assume it belonged to the top-ranked player. At the 11th he made his third birdie in a row to get to five-under and within one. "Very British haircut", Spieth said. Kevin Kisner, who's staying with Spieth in a rental house, called the haircut "military-grade". Schauffele earned his spot in that three-way tie after a 67 that contained six birdies.
"How much did you pay?" one writer asked. My dad's half French, half German. That served warning, if any were needed, that the American is taking his defence of the Claret Jug extremely seriously. Winning here, in fact, would be one of the greatest stories this great game has witnessed. He's not played in this event since 2015 due to chronic back problems. There was no wind at all compared to the first two days.
"I think Spieth is due for an off day".
The finish was a bit untidy. He duffed his chip, then three-putted from off the green.
He got a lucky break at the last, where his pulled tee shot came within inches of landing in the Barry Burn. Guess who won on that occasion?
"The fact that I won past year, I think helps sleep a little bit", Spieth said. I played so well today. "I felt I really had control of the ball". Shaved on the sides, a little longer on top. "And 5 is definitely within reach". He had at least a share of the lead after each of three rounds at the PGA Championship last summer until a bogey on the 70th hole ruined his chances.
His ball stayed dry but with 246 yards left to the hole he made a decision to lay up from the rough before punching a 100-yard wedge to three feet and saving par.
Spieth said he had a simple motive for his pre-round trim.
"It was the day to be aggressive today. It doesn't feel real".