But Molinari wasn't finished yet and he brought the house down with a birdie at the final hole for a round of 69 and a total of 276.
Imagine typing those words three months ago.
The 42-year-old's hopes of a remarkable comeback after a turbulent spell in his life - during which he has encountered off-course problems with the break-up of his marriage and a run-in with the law - were alive and well on the back nine.
Woods underwent spinal fusion surgery in April past year and was arrested on suspicion of driving under the influence the following month when he was found asleep at the wheel of his auto.
"I don't know what my future holds for me."
His previous best finish in a major was tied second at last year's US PGA Championship, won by Justin Thomas.
But success at this Open, on the toughest links in the rota? It sounded like a Woods victory march as he strode to the green to complete a memorable round, and who knows what Sunday has in store when the winds are supposed to blow.
Out of nowhere - well, from 55 feet away - the Holywood native sank a massive eagle putt to go into a share of the lead. "It's more a day to make as many pars as possible". In the moment, it didn't seem like much, but then reports of Woods' official world ranking started to surface. He shot 72 and was in the group four behind. Jordan Spieth cost himself another chance in a major by failing to make a single birdie.
You can see it sticking out the back of his sweater vest below on the first hole.
Xander Schauffele was hacking his way through fescue.
This took him to within one shot of the lead.
"I've always wanted to battle it out in a major with Tiger".
"I'm sure anybody within four or five shots can win". "It didn't feel any different".
The first to congratulate him was Woods.
While others made early charges, McIlroy was dropping back. On Sunday, he drove into thick fescue on 11, then rocketed his second shot into the crowd, the ball ricocheting off a fan's shoulder, and then another's iPhone, and settling in more hay. Schauffele made double bogey on the next hole, leaving one in the wispy grass, another over the green. He followed that with a bogey and never caught up.
It capped off the best stretch of golf in his career.
Eleven of the pin positions were also located within five yards of the edge of the greens, including on the daunting 18th where the champion golfer of the year will be decided - either in regulation or via a four-hole play-off.
His 66 was his first weekend round in the 60s in the Open since 2007.
"Oh, it was a blast", Woods would say afterward.
"It's pretty emotional because they gave me some pretty significant hugs there and squeezed", Woods said.
The prospects of a remarkable 15th major title for Woods after he proved he could compete once more at the highest level. Woods, who has had four back surgeries in recent years, was spotted with kinesiology tape (or KT tape) on his neck before Round 1 on Thursday. "Hopefully, they will get as inspired as I was at the time".
The last of his 14 majors came at the U.S. Open in 2008.