Molinari's day began with an eagle at the first hole and ended with a birdie and champagne shower on the 18th green, as he became the first Italian in 26 years to win this event.
'It's amazing, really unbelievable,' said Molinari, who finished at 23-under- par 265 after his third straight bogey-free round.
Molinari's first career win comes one year after his older brother, Edoardo, won the U.S. Amateur Championship.
The last Italian to win the Italian Open was Massimo Mannelli in 1980.
'I wouldn't have thought of winning so early,' said the younger Molinari, 23. 'I was hoping to give joy to the Italian golfers, but I wasn't thinking of this year.'
Anders Hansen and Jarmo Sandelin both took runs at Molinari, but neither could do enough. They finished tied for second place at 19-under-par 269 -- Sandelin after a 65 and Hansen following a 66.
Soren Kjeldsen was fourth at minus-18 after a final-round 68, and Benoit Teilleria finished one shot back in fifth place following a 69.
With an enthusiastic crowd in tow, Molinari had another dream round, his fourth straight in the 60s. It began with a chip-in birdie at the par-5 first hole, which he played at 5 under for the tournament.
Molinari added birdies at the sixth and ninth to make the turn at minus-20, but his most critical stretch of golf came on the final seven holes.
Tied for the lead with Sandelin, Molinari missed a golden opportunity to distance himself when he three-putted for par at the 12th.
But Sandelin did the job for him when he missed a 10-foot par putt moments later at the 16th to fall one behind at 19 under. Molinari would be alone in the lead the rest of the way.
'I was quite nervous after I three-putted the 12th,' said Molinari. 'I saw Jarmo Sandelin was 20 under, too, so it was close.'
Molinari then knocked his approach shot at the par-4 13th within 10 feet and rolled in the birdie putt to move two shots clear of the field. At the 15th, he chipped within two feet to set up another birdie, moving to minus-22 for a three-shot advantage.
With his closest competitors failing to make birdies ahead on the course, all Molinari needed to do was play it safe for the win. But he continued to attack.
Holding a three-shot lead, he went at the flag stick on the 18th, even though the pin was tucked on the left side with water just feet away.
Molinari was showered with cheers from the gallery after that bit of showmanship, and a champagne shower followed after he made the putt, as well- wishers stormed the green to celebrate.
'I've never seen a crowd like this,' said Molinari, whose only bogey of the tournament came on a three-putt in the first round. 'It was great, like being in a football (soccer) stadium, more or less.'
Phillip Archer and Bradley Dredge tied for sixth place at 16 under after rounds of 71 and 68, respectively. Italian Alessandro Tadini shot a 68 and shared eighth place at minus-15 with Peter Fowler, Garry Houston and Marc Warren.
Being tied for the third-round lead with Molinari did Benn Barham no good. Playing alongside the crowd favorite, he stumbled to a 3-over 75 and finished tied for 16th place at 13 under.