Molinari, who finished at 8-under 276, raised his fist and shook it lightly before slamming it for emphasis.
Meanwhile, Fleetwood is the most likely to become the first English victor of the Claret Jug since Nick Faldo in 1992.
Schauffele, the PGA Tour rookie of the year last season, holed a 30-foot putt from behind the 18th green for a 67. Schauffele has two holes remaining.
All around him on a windy summer day on the links of Carnoustie, the leaders were imploding as Tiger Woods moved into the lead at the turn.
It was the first time since the 2007 U.S. Open that he trailed going into the final round of a major, had the lead and didn't win.
Woods had been surprised to find himself leading so quickly after starting the day four shots from the lead.
So did Woods. "It didn't feel any different to be next to the lead and knowing what I needed to do", he said.
Pepperell teed off at 11.40 a.m. local time with Phil Mickelson. Woods got a break by hitting someone in the gallery, but then left his pitch hanging precariously on the side of a pot bunker.
Spieth was tied for the lead with Schauffele and Kisner overnight but slipped away with a closing 76 to end four under.
Fresh from his best major round in seven years on Saturday, with the 42-year-old signing for a 66 on Saturday, Woods surged to seven under, with playing partner Francesco Molinari one further back.
Kisner, in a three-way tie for the lead, took double bogey on No. 2. But while they were all over par on the front nine, he made birdie on No. 4 and then added another on the par-5 sixth.
Sunday's result was not what numerous thousands who tracked through the humps and hollows of the links course wanted, though it probably was for the male spectator who heckled Woods as he hit his drive at the final hole.
Tiger Woods is out on the course, making a par on the first hole.
However, Tommy Fleetwood's chances of becoming the first English victor since Nick Faldo in 1992 looked to have gone after he pulled his third shot on the sixth out of bounds, the resulting double bogey leaving him six off the pace.
Carnoustie is still waiting on the one element that defines a strong test at the British Open: the wind.
Even defending champion Jordan Spieth seemed ordinary, in a round where he was doing some extraordinary things.
The Californian finished back on -5 but gave us glimpses of his best and hope that Major No.15 could be out there yet.
Only four of the first 60 players to complete their rounds on Sunday carded a sub-70 round.
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.
Spieth, at 24, is seeking to become the youngest player to retain the Claret Jug since Tom Morris jr in the 1870s.
Jordan Spieth has a share of the lead in the British Open and a big edge in experience.
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