"We found something late on Tuesday," Merritt said about the way he was setting the club before his shots. "I knew it was just off, and we finally found it."
Merritt had missed the last five cuts on tour.
"The ball striking has been fabulous the last three days. I didn't make any putts the first two days, but they went in today."
One shot back on the crowded leaderboard was Rickie Fowler after a 68.
Another stroke back were Americans Charles Howell III (67) and Jason Bohn (67), Sweden's David Lingmerth (68) and 23-year-old Kim Meen-whee of South Korea (67).
Japan's Ryo Ishikawa, who led by one after the second round, shot a 71 and was tied for eighth at 11-under along with Briton Justin Rose (65), Carl Pettersson of Sweden (64) and American Bill Haas (64).
Woods, who began the day tied for fifth, three shots off the pace, plunged to nine behind after posting 74.
He shot 66 in Friday's second round for his lowest score in relation to par this year and found himself in the hunt, a rare occurrence in his dismal season.
But the 14-times major winner, coming back from back surgery and another swing change, was wild off the tee, missing his first six fairways and hitting only 10 of 18 greens.
Woods, whose world ranking has plummeted to 266th, has recorded three missed cuts, a withdrawal and just one top-25 finish in eight starts on the 2014-15 PGA Tour.
Merritt, making his 96th PGA Tour start, carded five birdies in a row out of the gate, then added a four-birdie run from the 12th in his brilliant round of 11 birdies and a lone bogey.
Chappell, playing his 136th tour event, was keeping it simple.
"I've done a really good job of just functioning in the truths this week," he said.
"That's the grass, that's the sky, that's the hole and this is my ball. Shoot the low score tomorrow and I can win the golf tournament."
(Reporting by Larry Fine in New York; Editing by Greg Stutchbury)
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