Johnson, whose name already is on the claret jug from his playoff victory at St. Andrews three years ago, holed a 30-foot birdie putt Friday on the 18th hole at Carnoustie for a 4-under 67 just as the rain was starting to end.
He begun the day in a three-way tie with fellow Americans Xander Schauffele and Kevin Kisner, two strokes clear of the field, but slumped to tied ninth place with a five-over 76 as a strong westerly breeze blew him off course.
In scenes reminiscent of those in the prime of his career, waves of excitement rippled through the massive gallery as 14-times Major champion Woods charged up the leaderboard.
That news arrived as Woods was playing a stunning bunker shot at the 10th to scramble a par, with Molinari - going quietly about his business with 11 consecutive pars - now his closest challenger alongside Spieth. The 35-year-old Italian was the hottest player in golf in the two months leading up to the British Open with two victories and two runner-up finishes.
Kisner, who has been at the top of the leaderboard all week, is aiming for a wire-to-wire win, and the form he showed while compiling a 68 on Saturday should serve as a warning to his title rivals.
"Just got to try to turn it around for the weekend", he said.
Seven players had a share of the lead at one point.
"The only thing they've seen is my struggles and the pain I was going through".
Woods shot 71 in the final round, finishing tied for sixth place at 5-under par and three shots behind the victor, Italy's Francesco Molinari. The combined age of Schauffele and Jordan Spieth, the two players in Sunday's final group, wasn't much more than Woods'.
Turkish President Erdogan comes to Ozil's defence
The third-generation Turkish-German was born in Gelsenkirchen and was a key member of his country's 2014 World Cup-winning side. Speaking to Anadolu Agency, Ozalan from the ruling Justice and Development (AK) Party, said: "I congratulate Mesut Ozil ".
Varadkar threatens to block United Kingdom planes from Irish airspace
We have seen the publication of the white paper , which was welcome, now the content of that white paper are in serious doubt". Prime Minister Theresa May will visit the Irish border tomorrow (Thursday) during a two-day visit to Northern Ireland .
Zaman sets records as Pakistan sweep Zimbabwe
Their in-form openers - Fakhar Zaman and Imam-ul-Haq laid the foundation for a big total by adding 168 runs for the first wicket. His opening partner Imam-ul-Haq was also in the runs once again, the pair producing their fourth century stand of the series.
"Momentum-wise, birdieing the very first hole, picking up where I left off, got me well into the round".
The 2014 Open champion bogeyed the 16th and 18th at Carnoustie to fall back to five under par, four shots off the lead heading into the final day.
Tiger Woods plays his second shot from a bunker on the eighth hole. Woods and Spieth were among five contenders to make double bogeys. "And he's like, 'I put my chips behind anything you decide, always.' And that kind of gave me that little extra boost", Spieth said.
And the Olympic champion carried on where he left off on Saturday, taking advantage of benign conditions to fire seven more birdies to match the 64s recorded by Steve Stricker and Richard Green the last time Carnoustie staged the Open in 2007.
"The way that Francesco played today was attractive", said Woods. He missed a short birdie putt and tapped in for par to finish off his final-round 71.
"I played pretty similar to this at the Players Championship". Rory McIlroy, pledging to "go down swinging" to rid himself of a bad Masters memory this year, had another 69 and was part of a large group two shots behind.
"I was in my own world", he said, though he saw when he got to the green that he needed to pick up another stroke. "I doubt he's been called Zach that many times".
England's Justin Rose is a shot behind Woods and McIlroy after earlier equalling the lowest score in an Open at Carnoustie with a brilliant 64, a day after needing a birdie on the last just to make the cut. And doing so a year after his fourth back surgery.
It was one of the few times Woods was out of position all afternoon in a round where he hit driver six times, compared with three times in the second round and once on Thursday.