He posted 2-under 69 Saturday afternoon in a round that included five birdies and three bogeys.
'Just hung in there and that was a grind,' Woods said. 'I got off to a sweet start. Stuffed it at the first and gave two right back at three and four, and just kind of hung around, hung around, hung around, and had a nice finish.'
Woods birdied his opening hole in the third round when he knocked it to a foot-and-a-half. He then gave shots back with bogeys at Nos. 3, 4 and 7. After seven, he didn't make another bogey all day.
He made the turn at 1 over, but a birdie at the par-5 13th for the second day in a row got him back to even par on the day and 6 under for the tournament.
Woods drove the green at the reachable par-4 16th, playing 289 in the third round. He knocked his 63-foot eagle putt to 8 inches and tapped in for birdie to get in red numbers on the day for the first time since the opening hole.
He closed out another birdie at the 18th when he knocked his approach to 11 feet and rolled that in.
Woods was noticeably stretching and wincing all day, but said he was going to get treatment for his back after the round, the same as he had been doing all week.
'It starts off great every day, and then it progressively deteriorates as the day goes on. Hopefully tomorrow it will be one of those days again and fight through it and see if I can win a tournament.'
Woods will tee off with Chappell at 1:40 p.m. ET in the second-to-last pairing.