McIlroy, the U.S. Open champion who has had three top-five finishes at this tournament, made three birdies in his first four holes but bogeyed two of the next four. He steadied with three birdies on his back nine, including a chip-in on No. 8 from just off the green.
Robert Karlsson of Sweden also had a 67. The pair were a shot ahead of Gareth Maybin of Northern Ireland.
Woods holed two birdies in a bogey-free 70, but struggled on the greens, missing several putts. Top-ranked Luke Donald shot a 71.