Molinari, who had taken considerable time off over the last few months to prepare himself for a busy golfing schedule in 2019, produced the best round of the day to win by two over third-round leader Matthew Fitzpatrick while Sungjae Im, Tommy Fleetwood and Rafa Cabrera Bello were another shot back in a share of third.
After holing the putt, he went to the locker room and watched on TV to see if his 12-under score would hold up.
The other two spots went to Sungjae Im, the 20-year-old South Korean who closed with a 68 and tied for third; and Honda Classic victor Keith Mitchell, who made eight birdies in his final round of 66 to tie for sixth. "But obviously when you get it done, then at the end it's a great feeling".
"I don't know, there must be something going on with that line, because it seems that a lot of guys winning the tournament make that putt", Molinari said.
"I said this after I won the Open Championship a year ago, I didn't enjoy it - that half an hour - at all and I didn't enjoy today at all watching the other guys", he said.
"I'm playing well", McIlroy said after a tie for sixth, his worst finish this year.
Molinari had four birdies on the front nine and four more after the turn, including a 44-foot birdie putt on the 18th hole that sealed his third PGA Tour victory.
The 24-year-old from Sheffield, who did not drop a shot in round three, made his first bogey of the final day at the 15th to fall three adrift with three to play. "But I think it's just been part of the process of, as a junior golfer I wasn't even the best golfer in Italy, so it's been a long journey since and step by step".
This time, he was in good position just one shot behind Fitzpatrick.
Harding was three shots off the lead at the start of the day and although he birdied three of the first four holes, bogeys at the sixth and seventh looked to have derailed his title challenge.
"I probably played too safe", the young Englishman said. "So it's still a bit unreal to think that I've done kind of the same today".
The Arnold Palmer Invitational is one of the PGA Tour's most prestigious tournaments - offering a US$9.1 million (AU$12.9m) purse and a three-year exemption on Tour for the victor.
Meeting with the media and donned in an Arnold Palmer red alpaca cardigan, Molinari toasted Palmer with one of the legend's favourite drinks, Ketel One vodka, on the rocks, with a twist of lemon.
And making putts ... and making putts.
The reason for that is - if a high-owned basketball player flops, he likely still provided you with some production, unless he left the game early or gets scratched.
It was more of the same on the back nine, with Molinari getting out of every pinch without dropping a shot.
PGA Tour officials confirmed on Sunday that Tiger Woods will speak to the media at TPC Sawgrass on Tuesday, a sign that the 14-time major champion is hoping to give it a go at the Players Championship on Thursday.
He joins Brooks Koepka, Justin Thomas and Gary Woodland with the most final rounds (four) of 64 or better on the PGA TOUR since the start of the 2016-17 season. "I took a longer break after past year".
Francesco Molinari is continuing to play the best golf of his career at age 36.