On his back nine he carded a further six birdies, parred one hole and dropped shots on two holes to come in with 32 shots played for his 63.
Five holes later, Woods threw another charge into the proceedings when he knocked his approach at the par-5 9th to 15, then holed the ensuing eagle putt.
With his swing of old back for the most part, Woods held the lead at the turn thanks to an eagle at the ninth and remained at or near the top until a poor drive and bogey at the last.
Englishman Justin Rose is alone in fourth at 8 under after a second consecutive 4-under 68, one shot ahead of a group that includes Woods, Matsuyama, Francesco Molinari, Matt Kuchar and Rickie Fowler.
It is still too early to start thinking about winning majors, or even this tournament, but for the first two rounds at least, it sure looked like Tiger is back. The next hole is par-four.
We should all probably sit down, take a deep breath, and try to temper our excitement about Tiger Woods.
"I think it is successful because I went out there and shot 31 on the front nine and built upon what I did yesterday", responded Woods when asked how he rated the round. Those are the internal struggles I haven't had for a while.
"I had a hard time all day with my speed on these greens", Woods said. "The greens they seemed to be a foot faster", he said after his round.
Meanwhile, Hoffman birdied each of the final five holes to finish off his stellar round.
Woods' layoff included his fourth back surgery, a DUI arrest from pain medications and a rehab stint. Today he is paired with Henrik Stenson. "I was playing with Justin and he's never played with Tiger".