Nitties, who also shot a 66 in the opening round, kept pace with the leader for much of the day with birdies on one, six and 14, but bogeys on 15 and 17 saw him slip three back.
American Kevin Na could have made it a three-way tie-off, but missed an eight foot birdie putt on the last and finished third on 271 while former USPGA champion David Toms and James Nitties were tied for fourth another stroke away.
Woods, who had a share of top spot after an opening six-under 66, produced an unspectacular but effective round of 68 to move to 10-under overall, three clear of Australia's James Nitties and Greg Chalmers and compatriot Jason Dufner, who was the best of the early tee-offs with a 67.