Woods, who has not led on the PGA Tour since winning the WGC-American Express Championship last October, finished nine-under on 135 at Quail Hollow Golf Club.
First-round leader Kirk Triplett (73), Notah Begay III (70) and Arron Oberholser (68) were joint second on 137.
Australian Stuart Appleby (72), Brett Quigley (72), Joey Sindelar (69) and Fijian Vijay Singh (70) shared fifth place on six-under 138.
Paraguay's Carlos Franco, Davis Love III, Kevin Sutherland, Canadian Mike Weir, Chris DiMarco, Joe Ogilvie and Cameron Beckman were all on 139.
U.S. Masters champion Phil Mickelson shot a second consecutive 70 and was among several players on four-under 140.
Defending champion David Toms followed his opening 75 with a 71 and missed the cut which fell at even-par 144.
After showing signs of his old form in the opening round, Woods made a few minor swing changes that paid big dividends on Friday.
"It's coming around," Woods told reporters of his game. "Today was a little bit tighter than it was yesterday and you want to just continue to improve on that.
"I certainly felt a lot more comfortable. Yesterday was a good sign, I just over-shaped the shots. That's easy to fix and I went out there today and shaped it less."
SWING ISSUES
While still having issues with his swing, Woods hit nine of 14
But the constant in his game has been his form on the greens. He took 25 putts in the first round and needed only 22 on Friday.
"I felt like I was putting well all day yesterday but they were all for pars," said Woods, back after a three-week break from the tour.
"Today I gave myself more looks at birdies. I made a nice putt on one, a little right to left, a nice 'bomb' (long putt) on two and from then on I made some really good putts."
Woods has gone on to win 20 out of 24 times when he has either held or shared the 36-hole lead, including the last 18 in a row dating back to the 1999 Memorial Tournament.
However, it has been a while since he has been close enough to the lead to make a difference to the outcome. Except for his WGC-World Match Play Championship victory in February, Woods has finished in the top-10 only three times.
"Considering the way I've been playing the last few tournaments, trying to come back from so far back, I've always been one that would much rather be ahead than coming from behind," he said.
"Hopefully I can get out there tomorrow and play just the way I did today and hopefully Sunday I'll do the same thing. This is only halfway. We have a long way to go."