Molinari, 33, had been four shots clear with six holes to play but U.S. Masters champion Willett, one of seven European Ryder Cup players competing in Milan, cut the gap to one with a birdie and an eagle at the 13th and 14th respectively.
"I had the ideal start, I couldn't start any better," said Molinari, who is not in the European Ryder Cup team that faces the United States at Hazeltine, Minnesota from Sept. 30-Oct. 2.
"When I birdied 12, I got four shots (clear) and thought maybe I could relax a bit and I got punished straight away. Coming in I had nothing left, I was just playing with my soul," added the 2010 and 2012 Ryder Cup player.
Molinari will collect 500,000 euros ($557,750.00) in prize money for his fourth European Tour win and first since the 2012 Spanish Open.
Spain's Nacho Elvira and Chris Paisley of England tied for third place at 18-under.
Germany's Martin Kaymer, who is in the European Ryder Cup team, finished 12-under and tied for 20th.
($1 = 0.8965 euros)
(Reporting by Alan Baldwin, editing by Ken Ferris)
