The 14-time major champion, 40, who shot a 65 on Friday, is eight under, 11 shots behind leader Hideki Matsuyama.
The world number 898 began with four birdies in the first five holes before falling away on the back nine.
For three straight days I've gotten off to great starts - for two of those days I haven't been able to keep it going
The American's last PGA title was the Bridgestone Invitational in 2013.
He has not played competitively for 466 days, during which time he had two back operations.
Woods kicked off his comeback this week with an opening-round 73 before the brilliant seven-under 65. On Saturday, the former world number one looked set to emulate his second-round feat after moving to five under for the day after 12 holes - but bogeys on 13 and 14 meant he dropped back.
He then found the water on the approach to the final hole as he finished with a double bogey.
"For three straight days, I've got off to great starts," Woods said. "For two of those days, I haven't been able to keep it going."
Japan's Matsuyama carded six birdies and an eagle on his way to a stunning round of 63, which gave him a seven-shot lead. US Open winner Dustin Johnson and Open champion Henrik Stenson are behind him on 12 under.
The Hero World Challenge, hosted by Woods, is an unofficial money event on the PGA Tour but world ranking points are up for grabs.
The invitational event involves 18 players and includes three of this year's major winners - Johnson, Stenson and Jimmy Walker - and 2015 double major winner Jordan Spieth.
Olympic champion Justin Rose, playing his first event after a seven-week break, withdrew with a bad back before play got under way at the four-round event in the Bahamas.
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Tiger Woods is on course for a good finish in his first tournament in more than a year after posting a two-under-par 70 to lie 10th going into the Hero World Challenge final round.