"With the chances I had and the way I played, I was looking for a little bit better," Stenson told local media.
Woods, an eight time winner, birdied the 18th for a 69 and a share of 10th at 209.
"That was a nice one," the former world number one said of the birdie. "Maybe a low (score) tomorrow will give me a chance to kind of steal one."
He will need to overcome some of the world's top players.
While DeChambeau, the second-round co-leader, hung on for second with a 72, McIlroy, Rose and Fowler are all well placed.
Northern Irishman McIlroy, playing his best golf in the United States this year, was strong on a back nine which featured an eagle at the 12th. He finished the day outright third at 10-under after his fourth birdie in a round of 67.
"It was great to get an eagle there, especially after coming off the bogey on 11," McIlroy said. "It was a big momentum shift."
He also enjoyed his birdie at 18.
"I didn't feel like I got a lot of perfect numbers. I was sort of in between clubs a little bit so to persevere and get a good one at the last and put a good swing on it and take advantage was really nice."
Englishman Rose (67) and American Ryan Moore (69) were a stroke back on nine-under.
"I hit loads of greens, loads of fairways today," said Rose, who had six birdies and a bogey.
"That was as clean a ball-striking round as I have had all year, so I am excited."
Fowler was in a group at eight-under. He managed a 70 despite dropping three strokes in a meltdown on the last two holes.
The American, who was once tied for the lead, had a bogey at the 17th and a double-bogey at the last.
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Ian Ransom)
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