Jim Furyk, who shared the first-round lead with Ben Curtis and Todd Fischer, managed a 1-under 70 to join Tim Herron and Duffy Waldorf at 8-under-par 134. Curtis was one shot further back at 7-under-par 135 while Fischer followed at 6-under-par 136 along with Steve Flesch.
'I played a little bit better today, but more importantly I putted better,' Woods said.
Woods played the back side first and collected a birdie at the par-5 11th before a bogey at the very next hole dropped him back to two-over. Woods answered with an eagle at the par-5 15th and a birdie at the par-4 18th to make the turn at 1 under.
The reigning Masters champion found trouble with a bogey at the par-3 second, but he got that shot back with a birdie at the par-4 fifth. At the par-4 seventh, Woods played his second shot inside 2 feet and tapped in for a birdie. He then drained a 10-foot putt for a birdie at the par-4 eighth to finish at 3-under-par 139.
'You just stay in the present,' said Woods. 'You work on what you have to do to get the ball to the next spot, and that's it. It doesn't get any more complicated than that. You just try and place the golf ball where you need to try and place it at all times and try and stay as focused as you possibly can at that moment, and forget the rest.'
Couch, a two-time winner on the Nationwide Tour this season, parred each of his first nine holes before running off back-to-back birdies starting at the par-4 10th.
The 32-year-old, who owns five career titles on the Nationwide Tour, two- putted for a birdie at the par-5 15th to reach minus-8. then dropped his second shot inside 4 feet and converted the short birdie try to secure the 36-hole lead.
'My goal coming into the week was to make the cut and take advantage of what they did for me, and that's happened,' said Couch, who is playing under a sponsor's exemption. 'So far a little better than that, so hopefully I can have a good weekend and a good outcome.'
Furyk struggled early with a pair of bogeys over his first five holes. The former U.S. Open champion countered with back-to-back birdies from the eighth and rolled in a 5-foot putt for a birdie at the 11th to get to 8 under.
Furyk was unable to make a move down the stretch, however, and parred his way in to finish one shot back.
Herron started on the back nine and birdied his first two holes out of the gate. Herron stumbled to back-to-back bogeys from the 12th, but responded with three consecutive birdies starting at the 14th.
He added two birdies on the front side for a round of 66.
'I got the ball up and down pretty well, hit some good trouble shots,' said Herron, who hasn't won since the 1999 Bay Hill Invitational. 'I felt like I kept it going, which will be more positive and beneficial going into the weekend.'
Waldorf also started at the 10th and birdied each of his last three holes for a round of 65 and a share of second place.
Chad Campbell and Scott McCarron share eighth place at 5-under-par 137. Shaun Micheel, Stuart Appleby, Brian Gay, Craig Perks, Jonathan Byrd, Brett Quigley and Ted Purdy are knotted at 4-under-par 138.
Defending champion Stephen Ames shot a 71 to finish at 1-under-par 141. Vijay Singh followed on the cut line at even-par 142 after a round of 70. Among those who failed to make the cut were John Daly, Mike Weir, Ryan Moore, Charles Howell III and Peter Lonard.