The world number two carded seven birdies and only two bogeys to end the day in a commanding position, despite his Northern Irish playing partner recording two eagles today.
Woods started off with a tap-in birdie after his eagle putt just stayed up on the par-five opener. He matched that score at the second and third and, though he gave a shot back at the fifth, a fourth birdie after a superb approach to the long eighth took him to 16 under for the tournament.
He birdied the 10th after his approach bounced just over the hole and added another at the par-three 15th, and though he dropped a shot at the penultimate hole he responded at the last to close on his second win of the season, and the 76th of his career.
Northern Ireland's McDowell eagled the first and picked up further shots at the third and sixth to stay hot on the heels of the world number two up to the turn.
Things did not go so smoothly on the back nine, with a bogey at 11 and a double-bogey six at the 14th, but he undid some of the damage at the 16th.
Having driven almost 320 yards to the fringe of the green, McDowell chipped in from around 20 feet for a superb eagle on the par four.
But he failed to take advantage of Woods' error at 17 when his birdie putt stayed up, and a monster birdie attempt at the last also refused to drop.
Phil Mickelson and Steve Stricker ended the day sharing third place after each shooting 69 to finish 13 under.
The former took a double-bogey six at the third to cancel out his two front-side birdies, but picked up three more shots in an unblemished inward nine.
Stricker opened the back nine with his third birdie of the day, offset only by a dropped shot at the seventh, and another bogey at 15 was immediately cancelled out at the next.
Spain's Sergio Garcia birdied two of the last three holes to share fifth place on 11 under par alongside Michael Thompson - last week's Honda Classic winner matching Garcia's round of 67 - Keegan Bradley and Charl Schwartzel.
Bubba Watson was a further shot back, along with Sweden's Freddie Jacobson, while Ryder Cup team-mates Keegan Bradley and Jason Dufner were at nine under.
Justin Rose and Ian Poulter were the leading British players at six under as fellow Englishman Lee Westwood fell away late in his round.
Westwood made four birdies in five holes around the turn but four bogeys dropped him to a one-under-par 71, leaving him three under for the tournament alongside McDowell's compatriot Rory McIlroy after the world number one signed for the same score.