O'Meara made a fine birdie at his final hole to shoot a six-under-par 66 in a testing wind on the highly rated Cog Hill course on the outskirts of Chicago. He enjoyed a one-stroke advantage over Woods, Phil Blackmar, Jim Furyk and Dave Stockton Jnr.
Ben Crenshaw, the winner of the US Masters only two years ago, has pulled out of the Open Championship, which takes place at Troon in two weeks' time, while another former Masters champion, Fuzzy Zoeller, has decided not to try to qualify.
A toe injury and his father's poor health have forced Crenshaw out of an event in which he has twice finished runner-up. Along with Zoeller, fellow-Americans Robert Gamez and Duffy Waldorf have also withdrawn from final qualifying.