"It was a lot easier than I thought", Molinari told CBS television. "I thought that 10 under would have been a good score for me to end up at for the day, and I could have easily gotten that today on the back nine".
He is the first Italian to win on USA soil since Toney Penna in 1954.
Molinari matched the 18-hole course record with the lowest final round by a US PGA victor this season, his career low on the American tour by two shots.
"I grew up watching him play when I was in my teens and starting to think about turning pro", Molinari, 35, said of Woods.
Ryan Armour placed second at 13 under while Sung Kang shot a 6-under 64 on the day to finish in third at 12 under overall.
At the Memorial Tournament four weeks ago, Woods was well under par in both the second and third rounds, but he couldn't keep it going, settling for 67-68 and a tie for 23rd.
Missed birdie opportunities on the first two holes of Woods' back nine were followed by a blemish at the 13th, with the tournament host holing a six-foot gain at the 16th but then failing to get up-and-down from a bunker to save par at the last.More news: Notorious French gangster flees prison in daring helicopter escape
So Woods didn't outright say it, but that final comment appears to be a pretty likely jab at the U.S. Golf Association. "It was nice to make a couple birdies coming in". "Evidently, I would have to shoot 24 on the back nine". What Francesco did is awesome.
"Basically, just trying to get efficient hitting the golf ball and then getting comfortable hitting the ball down", Woods said.
The 14-time major victor ended with a final round of 66 and has only finished higher once since August of 2013, when he tied for second at the Valspar Championship in November.
Two-times European Ryder Cup member Molinari has been in recent sizzling form in Europe, beating Rory McIlroy to win the BMW PGA Championship outside London last month, so is not likely to be intimidated by Ancer on Sunday.
South Korea's Ryu So-yeon used a hot putter and a lucky bounce on No. 7 to seize a three-shot lead heading into the final round of the Women's PGA Championship on Saturday. He missed a 15-foot birdie putt at the fourth but landed his approach at the fifth 2 1/2 feet from the cup and tapped in for birdie. "And I was really happy, like, I couldn't help that". He made three more birdies and ended his round by missing a birdie putt from 8 feet.
Tiger Woods made a leaderboard charge before mistakes killed his momentum.
The fightback fizzled when Woods missed a six-foot birdie putt at the par-5 10th, then missed the green on his approach and made bogey at 11.