Idle for nearly 16 months while recuperating from two back surgeries, Tiger has a 36-hole score of 6-under and is tied with Rickie Fowler for ninth. Dustin Johnson and Hideki Matsuyama share the lead at 12-under with two rounds remaining
"I moved myself up the board," said Woods, who turns 41 later this month.
Tiger gleaned many positives from his opening-round 73 on Thursday, his first tournament action in 466 days. He birdied four of the first eight holes before slipping on the back nine.
Woods played alone Friday after Justin Rose withdrew with a back injury. Tiger could have requested a marker to fill his spot but elected to play by himself, finishing in two hours and 54 minutes.
Woods forged the first of seven birdies at the short par-4 first hole, smashing a big drive within 80 yards of the green before knocking a sand wedge to within five feet. He added another at the par-5 sixth, then made a great par-save at the par-3 eighth, where he pulled his tee shot into the sand dunes on the left, caught a favorable lie, then blasted a well-judged recovery that settled eight feet from the cup and converted.
Tiger laid up with a 3-iron at the par-5 ninth hole and it proved a smart strategy. He stuffed his third shot tight to the flag from 128 yards with a pitching wedge and polished off the tap in birdie to make the turn in 3-under 33 for the second consecutive day.
Woods kept it going on the back nine, recording back-to-back birdies on the par-5 11th and the 202-yard par-3 12th. On No. 11, he crushed a drive and had 5-iron in, two-putting from the collar. Tiger almost aced No. 12 with a 6-iron.
"I couldn't hit it any better," he said.
At the par-4 14th, Woods knocked his second shot 15 feet from the hole but faced a tricky 15-foot birdie putt. After consulting with caddie Joe LaCava about the break, the ball narrowly slid into the right side of the cup.
At the par-5 15th, Tiger busted his longest tee shot of the day and wound up just off the green with his second, two-putting for a birdie from long range.
Then came the save of the day. Woods drove into a rocky waste area on the right and only managed to gouge a 6-iron about 100 yards, remaining in the sand. From there, he flushed a solid third shot 25 feet past the flag and buried the putt, celebrating with a patented fist pump.
"That was big," Tiger said. "I wanted to keep that card clean. There's something really special about that."
He closed with stress-free pars.
"I really had it dialed in both ways," he said. "I was chipping it both ways, and I really had nice control of my [trajectory]. That was the key."
Woods had solid stats, hitting eight of 13 fairways and 14 of 18 greens. After using 26 putts Thursday with his old Scotty Cameron Newport 2 putter, he only needed 25 on Friday.
More importantly, he walked off the 18th green with a bounce in his step.
"It feels better today than it did Wednesday and Thursday, which is a very good sign," said Woods of his back. "I don't know why. Maybe it's because I made a couple putts."
A five-time winner of the tournament, Tiger will play the third round with Rickie Fowler starting at 12:26 p.m. ET on Saturday. The round will be televised by NBC.
Proceeds from the tournament benefit the Tiger Woods Foundation.