The world number one ended the opener on a one-over score of 71, with clubhouse leader Jim Furyk carding a 65.
Woods double-bogeyed on the final hole, but is adamant that he is still in with a shout of winning the competition.
"I'm still right there," said Woods, who has won five times this season," BBC Sport quotes him as saying. "As of right now I'm only six back and we have got a long way to go. I played really well today."
Great Britain's Lee Westwood put in a solid opener, finishing at four-under-par with a score on 66.