A stiff and sore Woods, the overnight co-leader, arrived at Sedgefield Country Club about three hours before his round to receive treatment on an undisclosed ailment.
Once he got onto the course he had superb control of his driver on the few occasions he used it, and even better mastery of his putter, holing a series of clutch par-saving putts throughout the day, but only three birdies.
"It was a grind today," Woods, who is in a three-way tie for second, told reporters. "Like yesterday, I kept leaving myself in tough spots above the hole and had to putt too defensively because of it. Consequently I didn't make a bunch of birdies."
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With a chance to join boyhood friend Gore in Sunday's final grouping, Woods's downhill, six-foot par putt lipped out at the par-four 18th, much to the disappointment of the huge gallery that followed him every step of the way.
The three-putt bogey, which capped a two-under-par 68, dropped Woods into a tie with fellow American Scott Brown (66) and Swede Jonas Blixt (62).
American Gore, who has known Woods most of his life, mixed nine birdies with one bogey for a 62 to vault into the lead at 15-under 195.
Woods acknowledged he would have to shoot a better score on Sunday to secure his 80th PGA Tour victory, which would leave him only two short of the record held by Sam Snead.
"It's not a course you can sit and make a bunch of pars and expect to win. You've got to go for it."
Woods, 39, whose world ranking has plunged to 286th as he has worked his way back after back surgery and swing revamp, has not won since the WGC-Bridgestone Invitational in 2013.
He needs to win here to be sure of qualifying for the FedExCup playoffs, which start next Thursday, though a solo second might get the job done.
Gore, whose lone tour victory came in 2005, showed a resurgence at the age of 41.
"Contrary to popular belief, I'm still a good golfer," joked Gore, who was playing so badly a couple of years ago he was ready to quit and take a coaching job.
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