Three more pars followed before Woods holed from 25 feet for birdie on the eighth, although another duffed chip on the par-5 ninth led to a first bogey of the day after reaching the edge of the green in two.
That left Woods tied for 10th at four-under 212, 10 strokes behind leader Charley Hoffman, in his first tournament in almost 10 months following spinal fusion surgery.
Hoffman was level par through eight on 12 under, leading Tommy Fleetwood by just one shot.
"I thought I did great", he told broadcaster Sky Sports. To come out here and score like I did was nice.
That was cancelled out by a bogey on nine, but further birdies on 10, 13 and 14 thrust him into contention before a wild tee shot on 15 led to a second bogey of the day.
"I did not know what I could do", admitted Woods.
Woods, who had a 69 at the Albany course on Thursday, made an impressive start to the second round with birdies on three of his first four holes. I blew majority past the hole. I had a lot of adrenaline going and I had to dial it back a bit.
Fleetwood is making his first start in the 18-man tournament and will look to cap his breakthrough season with another victory before getting married on Tuesday.
Said defending champion Hideki Matsuyama of Japan here on Wednesday, "I am sure Justin or Jordan (Spieth), we haven't seen his best of golf, but if he gets back to that point every week he will be the favourite and he will win a lot of tournaments".