Hoffman goes into the final round as the favourite, having taken a five-shot lead over Justin Rose (71) and Jordan Spieth (72), who are Tied-2nd.
On a blustery day, Woods fell back from a promising Tied-5th to lose five positions while Hoffman extended his lead from four to five shots in his tournament debut.
First round leader Tommy Fleetwood (74) dropped to Tied- 5th alongside Patrick Reed (71), Rickie Fowler (72), Matt Kuchar (72) and defending champion Hideki Matsuyama (72).
However on the course, it was all struggle for the 41- year-old tournament host until he recovered with birdies on 14th and 17th hole.
Hoffman may not have won since May 2016 when he took the Texas Open, but has had a great 2017. He had two second place finishes, two third place and as many other Top-10s in 2017 besides contending at the Masters and the US Open.
Hoffman and Daniel Berger who is in the back of the pack at Tied-16th while three others Rose, Molinari and Reed were under par with 71 each.
Woods, playing a third round in any tournament for the first time since the Hero Challenge last year, was hoping to get into contention.
He was three-under through four holes and 5-under through nine on Friday, he was 4-over in the first seven holes. He added a fifth bogey on 10th and was birdie-less till he arrived at the 14th.
"It's ridiculous it took me 14 holes to make a birdie," Woods said. "At that time, I'd already played four par 5s and nothing happened. Just one of those days. Anything I did right ended up in a bad spot, and then everything I did wrong, it was really bad."
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