The 14-time major victor was briefly the outright lead at Carnoustie on an absorbing final day as he makes an improbable bid to win his first major title since 2008.
Woods initially took advantage after playing the front nine two under, but it unravelled for the American great with a double bogey at 11 when he crashed a tee shot into the fans before fluffing a chip up to the green.
Despite a modest Open record, he had been backed on the strength of a fine few months that saw him claim the PGA Championship at Wentworth - his biggest win on the European Tour - and his maiden PGA Tour victory at the Quicken Loans Classic.
Woods made the most of his good fortune to make par. The 4-shot final-round deficit was his closest to the lead in a major since the 2013 Open at Muirfield, where he was 2 back but tied for sixth. That's what happened Saturday, when he shared the lead on the back nine and promptly made bogey.
At 5 under overall, Woods was two shots off the lead.
"Just like the ones I've practiced in my backyard", he said, adding, "That was big for me just to not finish with two bogeys on the last three holes, playing as well as I did".
The latter had been hoping to become the first player since Padraig Harrington a decade ago to retain the Claret Jug, but he faded with a final-round 76 to finish on four-under. The clincher was a bold drive on the 18th hole that flirted with edge of a pot bunker, a wedge to 5 feet and a birdie putt that made him a major champion. Rose is No. 3 and almost joined them until he made an 18-foot birdie putt on the last hole to make the cut on the number. "I need to try to keep it in perspective, because at the beginning of the year, if they'd have said you're playing the Open Championship, I would have said I'd be very lucky to do that". Woods moved into the top 50 of the Official World Golf Ranking, which qualified him for the final World Golf Championships-Bridgestone Invitational at Firestone. The words are written in gold on a plaque at Carnoustie and it is safe to assume that Francesco Molinari felt the same as his approach to the final hole sailed over the Barry Burn and stopped three feet from glory.
Tiger Woods couldn’t quite produce the miracle he was hoping for
England's Tommy Fleetwood began the day four shots off the lead and gained a shot on the first but his challenge began to evaporate with a bogey-double bogey-bogey run before the turn.
It capped off the best stretch of golf in his career.
"I've had a chance to win".
The document said Woods then failed four field sobriety tests, saying he was on four prescription drugs.
Tiger Woods admits contending at the Open felt just like the old days and was delighted his two children finally got to see what all the fuss was about.
Another dropped shot followed at the next hole and Woods was unable to recover. Schauffele made double bogey on the next hole, leaving one in the wispy grass, another over the green. "From someone like me coming from Italy, not really a major golfing country, it's been an incredible journey". As The Post's Chuck Culpepper notes, through three rounds, the leader board has 19 guys within five shots of the lead, seven major-title winners within those 19, 26 major titles between those seven.