Woods arrived at all three of this year's majors with high hopes after promising finishes. There was no wind at all compared to the first two days.
Not many people imagined it would be the unassuming Molinari who would quietly assemble another brilliant round - no bogeys all weekend - to claim the British Open for his own.
A two-putt from eight feet saw Woods slump back to five under and one behind what was now a four-way tie for the lead, with Spieth, Molinari, Kisner and Chappell in that group.
Spieth was at 9-under 204.
Spieth, the victor in 2017, Kisner and Schauffele went into the final round at 9-under-par, with a two-shot lead, while Woods lurked four back.
Tiger Woods has shot a 5-under 66 in the third round of the British Open and is in contention to win his first major in more than 10 years.
I couldn't watch Xander play the last two holes, to be honest. That turns the hole into a par 4 really.
Tiger Woods took the lead on Sunday at a major for the first time in nine years and lost it with one bad swing.
Brooks Koepka is unlikely to be celebrating back-to-back major victories at the British Open on Sunday.
Koepka is 3 over for the tournament, 10 shots off the lead. He is even par overall.
Woods flinched when it mattered most, the nerves of a 42-year-old on display for all to see.More news: Military fans out across Pakistan ahead of election
The 14-times major victor had to settle for a closing 71 and a 279 aggregate.
Molinari virtually clinched the title with a driver that skirted the edge of a pot bunker, leaving him a lob wedge from 112 yards that he hit to 5 feet.
There is no question that Tiger Woods is a contender once again and that is all that matters.
Francesco Molinari after completing the 18th hole. I knew the front nine with today's wind would play mostly into the wind, so pars were great. There already was a 64 on the board by Justin Rose and a 65 by Yusaku Miyazato.
Zach Johnson and Kevin Kisner shared the overnight lead at 6-under par.
Francesco Molinari has set the clubhouse target at 8-under par after shooting a bogey-free, 2-under 69 at the British Open.
Reputed to be the toughest links in golf, especially in the 20 miles per hour gusts that finally arrived Sunday, Molinari stopped playing the Dunhill Links Championship because that one stop on the three-course rotation ate him up. Rahm shot a second round 78, but the birdie on the tough 18th hole was little consolation for his week's work. Although he isn't necessarily expected to catch Nicklaus like he once was since battling a slew of issues - culminating in back surgery - every time Woods comes close to No. 15 people can't help but start to murmur: Is Tiger back? Fleetwood, who dropped three shots in two holes on the back nine on his way to a 71, is part of that group. He had to scramble to make birdie on the day's easiest hole, the short par-5 14th hole, but his 20-foot birdie putt kept his chances alive.
He then fluffed his first chip which came within inches of finding a bunker, and he then putted six feet beyond the hole before missing the return to walk to the next tee with a six on his card. "I knew I was within one".
The third round began with little more than a mild breeze, and several players were taking advantage.
Further trouble and another dropped shot was to follow at the next and it was with his head bowed deep in thought he strode down the par-three 13th where he managed to stem the haemorrhage with a par.