Woods was two shots back at four under. So was Rickie Fowler, whose eagle on the par-five No. 2 hole and consecutive birdies at holes No. 9 through 11 left him five under on the round.
McDowell, a former U.S. Open winner who won the World Challenge in 2010 by defeating Woods in a playoff, shot a two-under 34 on the front nine holes amid an intermittent drizzle.
The 18-player tournament, which pays $1 million to the winner, benefits Woods' charities and Woods has won the event five times, including last year.