Molinari led by two shots from Tiger Woods going into the final round at Augusta National.
The 14-times major champion reached the turn at one under on the day and then, right after his tee shot at the par-three 12th stuck five feet from the hole, had to wait out a 30-minute suspension in play due to lightning in the area.
Brooks Koepka, who won a second straight US Open title a year ago then held off Woods to win the PGA Championship, was alone in fourth on 206 after a three-under 69.
Woods brought the roars back to the famed venue with a brilliant four-under-par 68, putting himself on track for a fifth Green Jacket. Woods made birdies at both par-5s on his way to the clubhouse, before grabbing a share of the lead at 11-under par with a sensational tee shot at the par-3 16th and a seven-foot birdie putt. Woods became the second-oldest to win the Masters, again behind Nicklaus who was 46 when he won in 1986.
Finau equalled the all-time Masters scoring record on the first nine, helped by a magnificent 2nd shot at the par five eighth that left him with a tap-in eagle, leaving him in a tie with Woods for second. The 43-year-old ended his 11-year drought at major championships with a stellar final round to finish at 13-under overall and emerge atop a crowded leaderboard. The 28-year-old Koepka, a three-time major victor, made birdie on No. 18 to salvage a 71 and stay tied for the lead.
At one stage following his fourth back surgery, Woods fell to number 1,199th in the golf world rankings.
"I was literally just trying to hit the ball short", he said.
"This is definitely, probably one of the greatest comebacks I think anybody's ever seen", Koepka said, before rattling off Woods' total PGA Tour victories and 15 majors.
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"My plan for tomorrow is to go out and do the same", Molinari said. "To let them see what it's like to have their dad win a major championship, I hope it's something they'll never forget".
Any other time, a hobbled Day might have might have been the story after getting up off the deck to shoot five-under 67. "It wasn't about chasing, it wasn't about doing anything, it was just about going out there and executing the shots that I needed to".
"Mentally was very good", he said.
Former Golf Channel statistician Justin Ray highlights Molinari's wonderful recent run in majors, pointing out the Italian is combined for 31-under across his last 163 holes played in majors.
He had a chance to win the PGA Championship in his last major until Koepka pulled away and Scott made a careless bogey at the end to finish third.
Molinari drained a 13-footer on the first hole, before producing brilliant up-and-downs on the fifth, which Woods and Finau bogeyed, and sixth to stay at 13 under.
He shot rounds of 75 and 73.