Bradley said: "I had a tough finish last week [he shot 74 when in contention for the World Golf Championships-Bridgestone Invitational in Akron], but a lot of people have been great to me since and it's because of them that I was able to fight back."
Dufner added: "Those are tough holes, but it was disappointing. There's a lot to be learnt from this."
How it was Bradley and not Dufner almost defied belief.
The 25 year old looked to have blown his chances of becoming only the second player since 1913 to win on his Major debut when he triple-bogeyed the short 15th.
But the World Number 108 birdied the 16th and then made a near 40 footer for another at the 160 yard 17th.
In the group behind, meanwhile, World Number 80 Dufner also went in the water at the 259 yard 15th and, 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.
Suddenly they were level on eight under par and after both parred the last - no mean effort with the lake in play for the first and second shots - to beat Dane Anders Hansen by one, they returned to the 16th.
Dufner almost holed his second shot, but Bradley also hit in to within five feet of the flag and he was the one to make the birdie putt.
A par was good enough to make the gap two as Dufner three-putted the 17th once more and, although Dufner made a brilliant birdie on the last, Bradley's par secured the title.
Before Curtis, the last player to win a Major at the first attempt was Francis Ouimet at the 1913 US Open Championship.
Swede Robert Karlsson felt the pressure, just like Dufner. He had been one behind, but bogeyed the last three and allowed Hansen to come third after a closing 66.
“Very proud of myself,” said Hansen. “Obviously you play a Major, it's tough, the course is set up tough. I thought my ball striking has been good all week.
“I played really, really solid from tee to green and the putting has been pretty solid. It has not been magnificent but it's been pretty solid so all in all, it's good for my confidence - it's good for the future.”
The shock was that on the first three days, Dufner was three under par for holes 15 to 18, two better than anybody else in the field. But they got him in the end just like they got just about everybody else at some stage.
Luke Donald and Lee Westwood finished joint eighth, their late errors in the third round proving too much to recover from.
World Number One Donald, so annoyed at himself for double-bogeying the last hole of his third round and falling six behind, was only three back after playing his first 12 holes in four under.
But he went in the water on the short 15th - start of the fearsome closing stretch at the Athletic Club - and bogeyed the last as well for only a 68.
World Number Two Westwood also finished three under par and also bogeyed the last - his only dropped stroke of a day when he once more could not get the putts to drop.
Westwood, playing his 55th Major, said: "I played lovely again today. It's just one of those things.
"I felt like I stroked it a little bit better, but, having said that, I missed twice inside six feet in the first five holes.
"When you're looking to get off to a quick start that is not ideal. Then it was in the water at six and I made a nice 10-footer there for par.
"I didn't really hole that much, apart from ten feet on ten.
"I have enjoyed playing great for a long time now, but unfortunately when I turn up to majors and I don't win it's a disappointing week for everybody it seems - and obviously for me."
Donald commented: "It was a missed opportunity again. At the beginning of the day I thought if I could get to six or seven under I might have a chance.
"But the guys out front really made it tough - they are playing well - and I thought I had to press a little bit hard and take on some pins on those last few holes.
"Obviously I hit a poor shot on 15. I just didn't strike it well enough."