Woods was steady rather than spectacular as he compiled a two-under-par 70 in a capricious breeze at the Muirfield Village course. He stood at 12-under par 204 with one round left, while Fiji's Vijay Singh was alone on 206 after a round of 71.
The American Dennis Paulson shot 69 to trail by four strokes, while the world No 1, David Duval, also with a 69, was among a group five shots back.
The Spanish teenager Sergio Garcia slipped out of contention with a 74 that left him seven strokes off the pace, but he was poised, barring a disastrous final round, to earn enough money to secure his PGA Tour membership for the rest of the year.
Woods, who won the TPC of Europe in Germany two weeks ago, says he is playing better now than when he won the Masters by 12 strokes two years ago.
"No doubt about it." he said, when asked whether he was a better player now than ever before. "I've got more shots, more control. My misses aren't as bad. The changes I've done over the past couple of years... I'm starting to see the benefits."
The American Juli Inkster took a grip on the US Women's Open title as the British challenge faded in the third round at West Point, Mississippi.
The Scottish player Catriona Matthew, who started just three off the halfway lead, slipped back with a 74 for a five under par 211 and finished 10 behind the veteran Inkster, who shot a 67 for an Open record 54-hole total of 201, 15 under par. The Californian will go into today's final day ahead of the Canadian Lorie Kane.Reuse content