The 35-year-old from Turin underlined his status as the hottest player in world golf by finishing with an eight-under total of 276.
Molinari, playing alongside former world number one Tiger Woods in the final round, produced a joyful first-pump and hugged his caddie after holing a five-foot birdie putt at the 18th hole.
It was the Italian's third victory in five starts. He also ended as runner-up in the other two tournaments.
Woods appeared ready to end his 10-year victory drought in majors midway through the round. The American topped the leaderboard until his hopes nosedived following a double-bogey at the 11th and another dropped stroke at the next hole.
The 14-times major winner had to settle for a closing 71 and a 279 aggregate.
"The way Francesco played today was beautiful," said Woods after ending in a tie for sixth spot.
England's Justin Rose (69), Rory McIlroy (70) of Northern Ireland and American duo Kevin Kisner (74) and Xander Schauffele (74) finished in joint second place, two shots behind the winner.
(Editing by Martyn Herman)
