Hoffman, who was seventh over night, carded a 9-under 63 for a three-shot lead over Jordan Spieth and Tommy Fleetwood, who finished the day Tied 2nd with a 5-under 67 and 3-under 69 respectively.
Woods was Tied 5 alongside four others but would have finished higher if it was not for the bogey on the 12th and 18th hole. The 41-year-old was in red hot touch on the front- nine, firing three birdies and an eagle for the sole lead before faltering on the back-nine to finish with 4-under 68.
The performance was commendable considering Woods has not won since 2013 and has played just three competitive rounds this year.
Woods, who shot three-under 69 on the first day, was on fire from the start. He smashed a 335-yard drive and placed his approach shot five feet from the pin for a birdie start.
More From This Section
Then came the fourth, which showed that fans just might get back the Tiger of the old. He smashed another drive down the middle and aimed for the flag on second to get to four feet for birdie number three of the day.
He missed a birdie from 12 feet on par-5 sixth where he missed the fairway for the first time and on seventh, he saved a good par after going into left rough and then into the bunker with his second. He saved another par on eighth.
Woods, who called the opening day as up and down, said round two performance was satisfying.
"I think it was successful because I went out there and shot 31 on the front nine. I built upon what I did yesterday, I cleaned it up. Only thing I really struggled with today was speed of the greens.
"Henrik (Stenson) and I were talking about it all day is that they seemed to be like a foot faster. I really did struggle getting the speed and I blew most of them well past the hole and made a few coming back. I also missed my share, too," he said.
"I felt like today I could have easily gotten to double digits under par. That would have put me probably one or two back, but I think I'm still in it. We've got two more days and I think it's supposed to blow a little harder tomorrow. If that's the case, I think a good solid round should get me up in there."
Earlier, Matsuyama had to wait for some time before he was cleared of a possible four-stroke penalty on the 18th hole.