But it was the 43-year-old's first Masters title since 2005.
With Finau also carding a bogey and Koepka dropping a shot at the sixth, Molinari suddenly found himself alone at the top of the leaderboard with a three-shot advantage.
"I think we picked the right shot and just didn't hit it hard enough, as simple as that".
"I didn't do it at Tampa, I didn't do it at The Open Championship, I was a little better at the PGA, but still I didn't win. My dad was here in 97 (when he won his first Masters) and now I'm the dad with two kids there".
"It's overwhelming because what has transpired".
"I really felt that I was starting to shape the golf ball, and my putting was starting to come around".More news: Astronomers capture first-ever image of a black hole
"A big "well done" from me to TigerWoods!"
Molinari had played near flawless golf through the first three rounds, carding a single bogey, but on Sunday a bogey along with the two doubles during a miserable final round of two-over 74 left him two back of the victor. "This is just fantastic!"
In a final round that was played in threesomes off both tees to stay ahead of approaching thunderstorms, Woods grabbed the outright lead for the first time with a two-putt birdie at No. 15. 79-year-old Nicklaus posted on Twitter.
He stiffed his tee-shot at the par-3 16th to tap-in range for a birdie, before a regulation par on 17 allowed Woods to bogey the 72nd - and he used all five strokes on that hole.
Yesterday's man is today's Masters champion.
Woods will move to No.6 in the world rankings - less than two years after he was ranked 1,199 and contemplated retiring from golf due to ongoing back injuries.