His hooked drive hit a tree off the opening tee, but he saved par from eight feet and then made a six-footer for par on the next after again going left and this time taking a penalty drop.
At the 350-yard third, his pitch finished just under 10 feet from the flag and he converted that to move into a large group on one under.
The former world number one has yet to make the cut on the course, but after an opening bogey he reached the turn in 34 and remained two under with seven to play.
Harrington started for home one under and Paul Lawrie joined him, Woods and a whole host of others by making eagle at the long 13th.
Ross Fisher birdied seven and eight, but a four at the short 12th put him one over again.