Woods then drove the green in two at the par-5 15 and tapped in for birdie to seize the lead alone at 13-under par then sank a four-foot birdie putt at the par-3 16 to stretch his advantage to two shots with two holes remaining.
Sunday's victory by Tiger was massive in more ways than one.
This is the first time Woods has ever come from behind on the final day to win a major championship, leaving him three behind Jack Nicklaus' record of 18 major titles.
"To have my kids there - it's come full circle".
The 43-year-old Woods started Sunday's final round joint second with fellow American Tony Finau, while Molinari was the man to catch, starting the day at 13-under 203.
Molinari scrambled hard on the front nine to maintain his overnight lead, making a number of clutch up-and-downs for par while hitting back from his first bogey in 50 holes at the seventh with a birdie at the eighth.
Paired together in the final round of last year's The Open Championship, won by the Italian at Carnoustie, Molinari and Woods found themselves in the last group again battling for a major title.
Lurking one shot further back is two-times defending U.S. Open champion Brooks Koepka, who will head off in the company of Webb Simpson and Englishman Ian Poulter, both four off the pace.
The 43-year-old has capped off a remarkable return to golf's top echelons following persistent back problems and troubles in his personal life, which almost led him to an early retirement from the sport he adores. But on Sunday it was Molinari who slipped up, with the 36-year-old from Turin finding the water at the 12th and 15th.