Seeking his first victory on the US PGA Tour after twice losing out in playoffs last season, Dufner carded a flawless seven-under-par 65 at the TPC Louisiana to post a 12-under total of 132.
Scotland's Russell Knox, a rookie on the US circuit this year who has made only two cuts in eight starts, fired a superb 64 to tie the course record and share second place with Americans Ken Duke (68) and John Rollins (66).
Australian left-hander Greg Chalmers also shot a 64 and was a further stroke back at 10 under, level with three-times Major winner Ernie Els (68) and American world number seven Steve Stricker (68).
Masters champion Bubba Watson, who clinched last year's New Orleans Classic in a playoff but has struggled with fatigue this week, birdied his penultimate hole on the way to a second successive 71 and made the cut right on the number.
"I'm very happy about it, I'm going to play two more days and re-evaluate my situation," Watson said.
"I'm exhausted. After the Masters win we really haven't had time to celebrate. I'm not really focused on golf."
The 35-year-old Dufner, with his distinctive pre-shot waggle, was among several players who took advantage of relatively calm morning conditions before the breeze began to pick up.
He birdied four of his first seven holes and picked up another shot at the par-five 11th before setting up his spectacular eagle at the par-five last with a five-wood from 236 yards.
"I had just a really good number for my five-wood to get somewhere on that green," a smiling Dufner said.
"Then I had a putt that was down-grain and breaking to the left with the grain so that was a nice way to finish the day."
Dufner, beaten in playoffs for last year's Phoenix Open and also the US PGA Championship in Atlanta, believes he is becoming much more comfortable when in contention.
"Maybe, this will be the week," he said. "I've had a lot of really nice finishes here on this golf course and feel pretty comfortable playing this golf course."
British world number two Luke Donald rebounded from his opening 73 with a bogey-free 65, covering four holes around the turn in five under to finish six strokes off the lead.
"It was certainly not quite as breezy as it was yesterday afternoon," the Englishman said. "The wind didn't really pick up until 16 ... so I had a good six holes without any breeze and made a couple of birdies.
"It's nice to post a low number and get back into the mix."
The cut fell at two under with former major champions Retief Goosen, Trevor Immelman and US PGA Championship winner Keegan Bradley among those failing to advance.