Furyk, who held the second-round advantage, posted a 3-under 68, while Baddeley carded a 5-under 66. The duo is knotted at 14-under-par 199 at Harbour Town Golf Links.
Billy Mayfair shot a 3-under 68 and is alone in third place at minus-11.
Ernie Els fired a 6-under 65 on Saturday and is tied for fourth place with Jerry Kelly, who fashioned a round of 5-under 66. The pair finished 54 holes at 10-under-par 203.
'You have to be pleased with that,' said Els. 'When you get it going on a roll like this, I want to keep it going. I feel like I'm playing well, and I might as well try to do the same tomorrow.'
Furyk and Baddeley were paired in the final group Saturday and both birdied the par-4 first. The young Aussie birdied two and the duo both birdied the par-5 fifth.
Furyk, the eighth-ranked player who won the 2003 U.S. Open blinked first. He hit a 5-iron into the right bunker at the seventh and failed to get up and down. Furyk drove into the trees and came up short of the putting surface with his second. His chip landed 7 feet short of the stick and he missed the par putt. The back-to-back bogeys left Furyk one behind Baddeley.
The pair made pars until Baddeley made a mess of the 11th. He drove right, then found the left bunker with his approach. Baddeley could not save par and fell back into a tie for the lead with Furyk at minus-11.
Both Furyk and Baddeley birdied the 12th and Baddeley kept his strong play going with a 19-foot birdie putt at No. 13.
At the par-5 15th, Furyk laid up with his second, then hit his third to 8 feet. Baddeley gave himself an easy chip from the side of the green with his third and he hit to 4 feet. Furyk holed his birdie try, but Baddeley pushed his right of the hole, putting the two back into a tie atop the leaderboard.
Each player hit a 9-iron into the 16th green and both recorded birdies - Baddeley from 10 feet and Furyk from 3 feet. Furyk reclaimed first at the par-3 17th when his 6-iron landed 11 feet right of the cup. He drained that putt, but found trouble at 18.
Furyk's approach at 18, an 8-iron from almost 180 yards, bounced into a back bunker. Baddeley missed right of the putting surface, but chipped to 3 feet, where he converted the par putt.
Furyk blasted out to 20 feet, but missed the par putt.
'That one didn't turn out the way I wanted to,' said Furyk, referring to his approach at 18. 'I've kind of forgotten all about it, because I hit it the way I wanted to. If I hit a poor swing it would be burning me a little bit, but because I hit the shot the way I wanted to it's easy to say, oh, well, and move on.'
The two will share the lead and the advantage on Sunday seems to belong to Furyk. He has 10 wins on the PGA Tour and has owned the 54-hole lead the same number of times. Furyk has advanced to the winner's circle half of those times, while Baddeley, who is winless on tour, has not won either of the two times he's owned a piece of the third-round lead.
'I don't feel like I'm out of my element or anything like that. I'm very comfortable where I'm at,' said Baddeley. 'I enjoy being in this position, and actually it feels like I haven't really been away from it. I feel very comfortable out there from the first tee onwards.'
Jose Coceres, the 2001 champion, managed a 3-under-par 68 on Saturday and is tied for sixth place with Lucas Glover (66) and Chris Riley (68). The threesome is tied at 9-under-par 204.
Tim Clark, the runner-up at last week's Masters, posted a 3-under 68 and shares ninth with first-round leader Vaughn Taylor, who carded a 1-over 72 in the third round. The pair came in at minus-8.