And he could get the battle with Tiger Woods he has always hoped for with the 14-time major victor among the chasing pack after a day of low scoring at a defenceless Carnoustie.
Playing alongside the resurgent Woods in the final round, Molinari carded a nerveless two-under-par 69 to win the Claret Jug by two shots from McIlroy (70), English hope Justin Rose (69) and Americans Xander Schauffele (74) and Kevin Kisner (74).
Tiger Woods started Round 3 six shots back of the lead, tied for 29th place at the British Open at Carnoustie.
"I've always wanted to battle it out in a major with Tiger".
Jordan Spieth says he will "expect the unexpected" when he tees off in the final pairing at the British Open on Sunday (July 23) 18 holes away from retaining the Claret Jug he won past year.
It's been five years since Woods' last win and a decade since he won a major. "I told them I tried and I said, 'Hopefully you're proud of your pops for trying as hard as I did, '" Woods said. "Either I hit that shot and it clears the burn, or I hit it right next to my feet", he said.
The 147th Open Championship delivered one of the most dramatic final rounds in major history on Sunday.
"We've got pretty much a new tournament tomorrow", Spieth said.
The 14-time major champion is 6 under for his third round.
The 23-time major victor finished runner-up last week at Wimbledon after giving birth to her first child late past year.
"Today was an interesting day", said Rose. I know I was within one. And even though I made that birdie on the second, which was a good start, I couldn't really capitalise on that start.
Tiger Woods is on the move in the British Open, edging to within a stroke of the lead on the front nine.
When Schauffele's par putt stayed out on the 17th the Italian puffed out his cheeks knowing only an eagle for the American at the last could deny him. So I think that was one of the key moments.
Molinari didn't drop a shot over the weekend at Carnoustie. That's why I went to the putting green because I probably would have felt sick watching on TV.
So, the sun is shining, everyone is bubbling with anticipation and on the eve of the event Bill Thompson, the captain of Carnoustie, says the Open has become too big for his town and the golf course he represents. He has birdied this hole all three days of the tournament.
"It certainly is possible", Woods said.
"I've got a chance in this", Woods said, beaming that ice-white smile. Rose's only major to date is the 2013 US Open, although he came agonisingly close at the Masters previous year before losing to Sergio Garcia in a play-off.
Woods, however, will not yet allow himself to consider how he might feel should he succeed. "The Tiger we have to face, he does things that maybe he didn't do (before)", McIlroy said. When I came here, I felt I was ready for the challenge. "Then ask me again".
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. "If I do that, a low round is very possible". I saw that Jason (Day) played a great round today, I saw that Brooksie (Brooks Koepka) played a really solid round today. You kind of feel a bit more grateful to be here rather than Friday night, [when] you feel frustrated to be there.