The world's top-ranked golfer is competing for the first time since arthroscopic left knee surgery two days after the Masters in mid-April.
His round began uncharacteristically with a double-bogey at the first hole.
Later, he rebounded by hitting one of the round's best shots -- a 190-yard bunker shot at No. 4 -- that set up the first of back-to-back birdies.
When his day ended, Woods was within four strokes of the 3-under 68s shot by Hicks and Streelman.
"We're all going to make mistakes out here," he told reporters about his start. "You're going to make more than two bogeys in 72 holes. I just happened to make two on my first hole."