Dufner, who equalled the lowest score in major history with a second-round 63, carded a closing 68 despite dropping shots at the final two holes, the 36-year-old finishing 10 under par.
Overnight leader Jim Furyk also bogeyed the 17th and 18th to finish two behind, Sweden's Henrik Stenson claiming outright third on seven under to go with his runners-up finish in the Open Championship at Muirfield.
Defending champion Rory McIlroy recovered from a triple-bogey seven on the fifth to card a closing 70 and finish in a tie for eighth place, one shot ahead of fellow Northern Irishman Graeme McDowell and Scotland's Marc Warren.
Lee Westwood, who started the day three under alongside McIlroy, struggled to a 76 to finish three over par.
"It probably has not sunk in," Dufner said. "I can't believe this is happening to me. To come back from a couple of years ago when I lost in a play-off feels really really good.
"I decided that I was going to be confident and put my best foot forward and play aggressive to try to win this thing. The last two holes were a little unfortunate but I am happy to get the job done and it's a big step in my career."
Beginning the day one shot behind Furyk, Dufner took command with some brilliant iron play, holing from four feet for birdie on the fourth and a matter of inches on the fifth, eighth and 16th to help erase the memories of his late collapse in the same event two years ago.
Dufner led by five shots in Atlanta after nearest challenger Keegan Bradley triple-bogeyed the 15th, only to find water on the same hole minutes later. After doing well to escape with a bogey there, he failed to get up and down from sand on the next and then three-putted the 17th.
Both men parred the 18th to go into a three-hole play-off which Bradley won by a shot to become the first player to capture a major with a long putter.
Furyk was aiming to follow Phil Mickelson as the second consecutive 43-year-old winner of a major and make amends for a nightmare 2012 in which he held or shared the lead after 54 holes in four tournaments and failed to win any, as well as bogeying the final two holes to lose his vital singles match to Sergio Garcia at the Ryder Cup.
He and Dufner began the final round with three pars before Dufner birdied the fourth from four feet and then made light of the treacherous fifth.
Mickelson, McIlroy and Ryder Cup hero Martin Kaymer were among the players who had taken triple-bogey sevens at the 437-yard par four, but Dufner's approach span back to within two feet of the hole for an easy birdie.
Furyk got back on level terms with an unlikely birdie from 35 feet on the next, but Dufner moved in front again with an even better approach to the eighth, this one almost spinning back into the cup and leaving a tap-in birdie.
Dufner saved par from six feet on the ninth and that was good enough to open up a two-shot cushion, Furyk finally hitting his first fairway of the day but then missing the green with his approach and failing to get up and down.
Further birdie chances went begging on the next four holes but Dufner then rediscovered his winning formula, spinning another shot back to within inches of the hole for a certain birdie on the 16th.
Furyk vitally kept the pressure on by holing from 12ft himself for his first birdie in 10 holes, meaning Dufner had to be satisfied with a two-shot lead with two to play.
A three-putt bogey from long range after Furyk had also dropped a shot on 17 meant the gap remained the same and both players bogeyed the last after coming up short of the green.
Stenson had moved to within a shot of the lead with an eagle on the fourth and was only two behind when he birdied the 13th, but crucially bogeyed the short par-fourth after hitting his second shot from a divot into a greenside bunker.
Playing partner and compatriot Jonas Blixt never really threatened after dropping shots at the first two holes but battled back to shoot 70 and claim outright fourth, one ahead of Scott Piercy and Masters champion Adam Scott.
Despite a birdie from long range at the third, McIlroy's hopes effectively disappeared when he missed from three feet for another on the next and then came unstuck on the fifth.
McIlroy was stunned to see his approach spin back off the green and onto the rocks on the edge of the water, but had to troop over to the drop zone from where he fired his fourth shot over the green and took three to get down.
The 24-year-old hit back with birdies on the ninth, 10th and 13th but knew the damage had been done.
"I actually didn't hit a bad shot, 168 yards to the pin, hit nine iron, pitched it just in the place where you can't pitch it I guess," he said.
"I saw a lot of great signs out there today. Hopefully I can just bring that through to the next few weeks and have a strong finish to the season."
Westwood had already bogeyed the second and double-bogeyed the third when he found water off the tee on the fifth, and although he managed to drop just one shot there, another bogey on the seventh soon followed.