Fifteen-time Major winner Woods, playing his first tournament since ankle surgery in April that followed his withdrawal from the Masters, shook off a bogey-bogey start to card a one-under par 71 that left him at even par, 16 strokes behind Scheffler and tied for 16th in the 20-player event he hosts at the Albany Golf Course in the Bahamas.
Woods said he'd been "pleasantly surprised" at how his body has held up, which was more of a concern than the state of his game.
"I still have game," he said. "It's whether or not the body can do it."
Woods, who turns 48 on December 30, had ankle surgery in April on the same leg that was severely injured in a 2021 car crash. While his leg pain is gone, he said he still contends with chronic back pain, but said before the tournament he could play as much as once a month in 2024.
On Saturday he started 10 off the pace and got off to an inauspicious start with bogeys at the first and second.
He clawed back with birdies at the third, sixth eighth and ninth -- where he got up and down from a greenside bunker -- before two bogeys and a birdie coming in. That included a seven-foot par putt miss at the 18th.
"It could have been a little better than the score indicates," Woods said. "I think I could have shot something in the high 60s. I think it was cleaner than it was yesterday."
Most importantly, Woods said, he was "very excited" at how he has responded physically to the pace of competition.
"To be able to knock off some of the rust as I have this week, showed myself that I can recover each and every day, that was kind of an unknown," he said. "I'm very excited how the week's turned out."
Scheffler cruising
Scheffler, meanwhile, was in cruise control, starting the day tied for the lead with Jordan Spieth and seizing control with a 15-foot eagle at the third.
He added four birdies before he rolled in a 14-foot eagle at 15 to push his lead to four strokes over England's Matt Fitzpatrick, who also signed for a 65.
A bogey at 18, where Scheffler's drive was in the right rough, cut that by one, giving him a 16-under par total of 200.
"I played really well today, really solid the whole day," said Scheffler, the 2022 Masters champion who has finished runner-up in this event the past two years.
"(It's) nice to see some putts go in. These greens can be tough to putt at times, but I'm rolling it good."
Fitzpatrick had climbed the leaderboard with four birdies on the front nine. After a double-bogey at the 11th he birdied 12 and 14 before draining a 47-foot eagle putt at 15.
He bogeyed 16, but closed with back-to-back birdies for a 13-under par total of 203.
"It was good for pretty much the whole round bar two holes," Fitzpatrick said. "Drive on 11 was just what cost me, obviously, a double. Outside of that, everything was good today."
American Justin Thomas was alone in third after a four-under par 68 for 205.
Spieth, who was playing catch-up after his bogey at the third dropped him three off the pace, finished with four birdies and three bogeys in his 71 for 206, tied for fourth with Australian Jason Day and Americans Tony Finau and Collin Morikawa.
