McDowell defeated Woods in a playoff to win this event in 2010, the same year he captured the U.S. Open at Pebble Beach.
He shot a 6-under 66 at the Sherwood Country Club to move to the top of the 18-player field at 9-under 135.
Keegan Bradley shot his second straight 69 and was tied for second with Bo Van Pelt and Jim Furyk.
Woods was alone in fifth place at 211 following a 69 that included four birdies in a five-hole stretch beginning at the par-4 ninth. He won the tournament a year ago, ending the longest victory drought of his career.
Nick Watney, who owned the first-round lead, shot a 73 and was tied for sixth at 212 with Rickie Fowler.
Notable deaths of 2014 [PHOTOS]