The Italian began the day five shots behind Matthew Fitzpatrick and Rory McIlroy but, as that pair struggled to make birdies, Molinari stormed up the leaderboard on the back of a brilliant display at Bay Hill.
A flawless eight-under-par closing effort, which was capped by him rolling in a 45-foot birdie putt at the last, set a clubhouse target of 12-under-par that no-one was able to match.
The 36-year-old won by two shots from Fitzpatrick, with Molinari’s Ryder Cup partner Tommy Fleetwood a shot further back alongside Rafa Cabrera Bello and Korea’s Sungjae Im.
“I tried to be aggressive from the start and it was nice to see quite a lot of putts dropping... especially for my standards,” said Molinari as he celebrated his second success in a regular PGA Tour event.
“I think it’s been the best putting round ever in my career. And it’s nice to do it, obviously in those circumstances, at Arnie’s place.
“And I don’t know, there must be something going on with that line (on 18), because it seems that a lot of guys winning the tournament make that putt.”
An opening birdie got Molinari’s charge under way before he registered another gain at the third when he hit his approach to seven feet to move to six-under-par.
He improved to seven-under with a birdie at the sixth and reached the turn in 32 courtesy of a stunning chip in from the rough at the eighth.
Molinari’s birdie trail continued at the 12th and 13th to move alongside Fitzpatrick at the top of the leaderboard.
He got on the par-5 16th in two before two putts helped him take the outright lead at 11 under and he sealed his stunning round with that monster birdie putt at the last.
McIlroy, the defending champion, had to settle for a share of sixth spot after a closing effort that contained just two birdies.
Matt Wallace finished alongside McIlroy, though the Englishman was left to count the cost after bogeys at the closing two holes.
Im’s effort secured him a spot in this summer’s Open Championship at Royal Portrush, where compatriot Sung Kang and American Keith Mitchell are also heading.
They all booked berths in the Claret Jug event through the Arnold Palmer Invitational being part of The Open Qualifying Series for the first time.