Baddeley shot a 1-under 70 in his final round and ended the tournament at 15-under-par 269 for his first PGA TOUR victory. He became the fourth Australian to win the event, joining Graham Marsh, Greg Norman and 2005 champion Peter Lonard.
Furyk, who entered the final round tied for the lead with Baddeley, carded two bogeys in his last seven holes. He finished with an even-par 71 to end at 14-under-par 270.
In a close, back-and-forth final round, the slim difference between first and second place came on the green: Baddeley needed 27 putts to finish his round, while Furyk needed 28.
'It came down to knocking in putts,' said Furyk, the eighth-ranked player in the world and a 10-time PGA winner, 'and he knocked in more than I did.'
Vaughn Taylor and Billy Mayfair shared third place at 13-under-par 271 after rounds of 66 and 69, respectively. Brett Quigley (67) and Jerry Kelly (70) were one stroke further back in a tie for fifth.
World No. 5 Ernie Els, the highest-ranked player in the field, shared seventh place with Tim Clark, last week's runner-up at The Masters. Els shot a 71 and Clark carded a 69 to reach minus-10.
The battle for first place was waged only between Baddeley and Furyk.
Baddeley was two shots ahead through six holes after birdies at the second, fourth and fifth holes.
At the par-3 seventh, Baddeley made bogey from a bunker behind the green to fall to 16 under, while Furyk made par from the rough to get within one shot of the lead.
It was a similar story at the par-4 eighth: Furyk saved par again from the rough, while Baddeley made his second straight bogey to fall into a share of the lead at minus-15.
Things changed briefly beginning at the par-4 10th, where Furyk rolled in a 45-foot birdie putt to reach 16 under and take the lead. Baddeley birdied 10, but then made bogey from a bunker at the 11th to drop two shots off the pace.
Baddeley pulled within a shot again after Furyk bogeyed the par-4 12th to drop to minus-15. He then tied his playing partner with a 21-foot birdie putt at the par-3 14th.
The gutsiest shot of the day came from Baddeley at the par-5 15th, where he went for the green in two with a 6-iron from 220 yards.
Cutting the corner, Baddeley hit over the trees and landed on the back of the green. His eagle try came up short, but he rolled in a 4-foot birdie putt to take a one-shot lead at 16 under.
Both players bogeyed the par-3 17th -- Baddeley from the right rough and Furyk from a greenside bunker. That put Baddeley at 15 under heading to the par-4 18th, with Furyk still one shot back.
Furyk landed within 10 feet on his approach shot, but missed his birdie putt just left. Baddeley pitched within 7 feet from the back rough, curled in the par putt and pumped his fists in celebration.
Maybe the only person happier than Baddeley was his wife, Richelle, who nearly ran onto the green before Furyk putted out for par.
'I was being patient and hanging in there, and today was just a great day,' said the 25-year-old winner. 'It's been a special weekend. It really has.'
After improving his performance each of the last four times he played this event, Furyk ended a runner-up for the second straight year (he was one of four runners-up to Lonard last year).
'I'm sure it was an exciting tournament to watch,' Furyk said. 'I just needed some of those putts on the back nine to go in.'