But it was the American's playing partner Molinari who wrote his own script to claim his major breakthrough at the 36th time of asking.
Woods shot a 5-under-par 66 in Saturday's third round that left him at 5 under through 54 holes and four shots back of the leaders. I knew I was coming in with some good golf. "I've had a career's worth in a few years", said Spieth, who admitted he found it "difficult" to hand over the Claret Jug when he arrived in Carnoustie on Monday.
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Jordan Spieth says he will "expect the unexpected" when he tees off in the final pairing at the British Open on Sunday (July 23) 18 holes away from retaining the Claret Jug he won past year. It will be interesting to see going forward, but this was his first taste of major championship drama for quite a while.
Woods led the field by one shot with eight holes to play, which was the first time he led a major on the final day since the 2011 Masters, but fell apart down the stretch after a pair of bad tee shots ultimately doomed him.
"The course bit me a few times the first couple of days, but then to go bogey-free over the weekend on a course like this is incredible".
With Schauffele recovering from four dropped shots in three holes on the front nine with birdies at the tenth and 14th to join him on seven under, Molinari got a birdie.
"But I'm right there". "I played patiently. Never got down on myself". With his third straight birdie of the round, Woods got to 5-under on the round and on the tournament. Woods was also close to birdies on the 13th and 15th but did escape damage on the 18th by making par after hitting the wall of the Barry Burn.
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Woods was at 7 under, in control of his game and hitting shots that only he can. Just when he took the lead and everyone's imagination began to swirl about what might be, he kicked away his best chance of breaking a decade-long drought in major championships. "The golf course was gettable".
McIlroy was left agitated by his finish, after bogeys on the 16th and last, dropped his back to a tie for sixth.
Molinari teamed up with his brother Edoardo in the Ryder Cup in 2010 and scored a half point against Woods to secure outright victory in his singles match in the 2012 competition in Chicago, dubbed the "Miracle of Medinah" after Europe fought back to win from a seemingly impossible position. Still in range, he couldn't get close enough for a birdie when it mattered.
Woods, however, will not yet allow himself to consider how he might feel should he succeed.
"Everybody will tell their horror stories and good stories, and we'll laugh and eat a big old meal and sit around and watching something stupid", Kisner said.
"It seemed like everybody was shooting six, seven under and I figured I could probably do the same and I needed to with the leaders starting at six".
Earlier, Justin Rose set the tone with the lowest score in Carnoustie's British Open history, a flawless 64.
Northern Ireland's Rory McIlroy after a bogey on the 18th during day three of The Open Championship 2018 at Carnoustie Golf Links, Angus.
Open runner-up Xander Schauffele insists he will look back on a chaotic final day at Carnoustie as a positive experience, despite missing the chance to win his first major.