The former world number one, also trying to play his way into the US PGA Tour's FedEx Cup playoffs, began yesterday tied for the lead at 11-under par.
He arrived at Sedgefield Country Club's 18th hole in sole possession of second place on 14-under, but a bogey at the last saw him drop into a three-way tie for second behind Gore -- who carded an eight-under par 62 for 195.
"I need to go out there tomorrow and make a run and get myself up there and make some birdies," said Woods. "There's a bunch of guys ... At 13 (under).
"There's a whole slew of guys at 12, 11, 10. Anybody can make a run and shoot the score Jason and Jonas did."
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The resurgent Woods -- coming off a missed cut at the PGA Championship that marked his third straight early exit from a major championship -- drew huge crowds on Saturday and he didn't disappoint.
By the time he birdied the fifth, he was tied for the lead with Blixt on 13-under.
Woods slid a 12-foot birdie attempt just past the hole at the sixth -- one of several birdie chances that failed to drop.
He also made several good par saves, including a 16-footer at the 10th.
"The putter just felt really good," Woods said. "My pace, I felt like I could be aggressive."
He rolled in a 12-footer for birdie at 16 to move within one shot of the lead, and made another par save with a testing four-foot downhill putt at 17.