Woods teed off on 10 and drained six-foot birdie putts at 12 and 13 and rolled in an 11-footer for another birdie at the par-four second hole.
Woods hasn't won since his seven-shot victory in the Bridgestone Invitational in August 2013.
"Very, very loud", Woods said.
He hit wedge into 7 feet below the hole on the par-5 11th, and another roar erupted.
Golf's dominant figure for much of the past two decades, Woods was the centre of attention once again at Palm Harbor on Saturday, with huge crowds gathering to see if the former world number one could continue a hugely encouraging week.
"We've got a long way to go", Woods said. I was living minute to minute. "I feel like I'm playing a bit better and cleaner. I did a lot of guessing - guessed pretty good, also got fooled a few times".
"It's fun to hear the crowd going insane again and realise how excited we are in having him back out here and play the way he is". "I've been ready to go".
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Woods chose to play at the Valspar for the first time right before the entry deadline.
He drained a putt from 22 feet for birdie at No. 10 underneath an overcast sky similar in color to his dark gray slacks and cap, contrasting Woods' bright pink Nike shirt that helped him stand out in a crowd even more than normal. But this was the first time he has holed a shot from off the green this year. He's made 10 previous starts on the PGA Tour this season and finished no better than 29th.
"I can confirm he's back". I've got a shot going into tomorrow. It's great. They get a little carried away at times and you've got to calm 'em down. Then he made his major mistake of the day, hitting over the green at the 13th, leaving him with a almost impossible chip that he left in a bunker.
Only four men beat Woods' score of 67, with Rose's five-under round putting the Englishman in the final group with Conners, who endured a stressful end to his round when his ball moved on the 18th green as he took a practice stroke.
These will be invaluable reps for Woods, who gets more comfortable with what his fused back will allow him to do every single round. Justin Rose (-8), Brandt Snedeker (-8), Patrick Reed (-6) and Adam Scott (-4) are among the other notable golfers firmly in the mix heading into what should be an entertaining final round.
In a tweet following the third round, Golf Channel's senior researcher, Justin Ray, provided a reminder of Woods' outstanding record when in contention on Sunday.