The world number one struck a superb second shot into the heart of the green and rolled in the putt to get to 15 under.
Chasing his 11th career major, Woods then parred the sixth to maintain his advantage and stay ahead of 2002 winner Ernie Els, who had briefly tied the American for the lead when he picked up his first shot of the day at the 528-yrd fifth.
American Chris DiMarco was alone in third at 12 after offsetting a bogey at the first with a birdie at the par-three sixth.
Argentina's Anders Romero, who booked his place at Hoylake after finishing as the highest non-exempt player at last week's Scottish Open, was a further stroke back in a tie for fourth after reaching the turn in two-under 33.
Romero had reeled off three consecutive birdies from the fourth before dropping his first shot at the par-three ninth.
Level with Romero were Sergio Garcia, who missed short putts to bogey the second and third to fall five shots behind playing partner Woods, and Australia's Adam Scott.
American Sean O'Hair birdied the last three holes for a 67 to hold the lead in the clubhouse at seven-under 281.
The 2005 PGA Tour rookie of the year, who tied for 15th on his British Open at St. Andrews 12 months ago, began the day 11 strokes off the pace.
SILVER MEDAL
Norwegian teenager Marius Thorp won this year's silver medal as top amateur, holing a 25-footer to birdie the last for a 71.
The 18-year-old from Oslo finished on even-par 288, seven strokes ahead of Italy's Edoardo Molinari.
Molinari, the only other amateur who made the halfway cut, closed with a 75.
Thorp mixed three birdies with two bogeys to finish level with playing partner and five-times Open champion Tom Watson.
"This is fantastic," said the Norwegian, who booked his place at Hoylake by winning last year's European amateur championship.
"I played really well all four days and today I played with one of the greatest legends in the game. It's been a perfect day."
Watson was also impressed by Thorp. "I think he's a very good player and he's fearless with the putter," the 56-year-old American said. "I remember those days. God I wish I could do that now."
