The 4&3 win was the only match in the fourth session of the biennial team competition to finish on a rain-affected day and helped push the United States into a strong lead by 11-1/2 points to 6-1/2 at Muirfield Village.
Dufner and Johnson had bogeyed the fourth to fall behind early on in their foursomes match and the Australian-South African combination then made a birdie at the par-four sixth to go two-up.
But birdies at the eighth, ninth and 11th holes gave the U.S. pair the lead and they ended up winning the last three holes, with Johnson holing out from the fairway for eagle at the par-five 15th.
Johnson modestly put his shot down to luck and also praised Dufner for the lay-up in the alternate-shot format after he had earlier driven into the rough.
"You're just trying to hit a quality shot and it seemed like Duf was going to hole out three times," said Johnson. "In about a three or four-hole stretch, his ballmarks were in a three-foot circle next to the hole.
"I guess if you just keep knocking on that door, maybe one is going to fall. There is a lot of luck involved. You can't deny that. It was a perfect number and I'm not embellishing because - the greens are so saturated that it was a half-shot.
"It was one of those shots, I could have got my 54-degree sand wedge there, but it would have spun, a lot. So it was kind of just a chip wedge that took spin off and landed right next to the pin and dropped," added the 2007 Masters champion.
It was a sweet way to end the day, particular after Johnson and Dufner had lost to Ausralian Adam Scott and Japan's Hideki Matsuyama 2&1 in their foursomes match left over from Friday.
The Americans, who had been five down, fought back with three straight birdies from the 13th hole before Scott and Matsuyama halved the next two holes to win.
U.S. captain Fred Couples then opted to leave Dufner and Johnson out of the fourball session before bringing them back for the final, alternate-stroke, session.
"When we had to come back out here this morning, we had our backs against the wall and we fought," said Johnson. "There were a couple lip-outs early in the round and a couple of burned edges ... and we would have kept on extending that match.
"But that was good momentum for our afternoon match. Even though we sat for a good while and ate four breakfasts, watched some football, and eventually went out there, we were hungry going into that last match.
"Getting done early just added more motivation. To win 4&3 , being down two through seven holes, I'm certainly proud of that and I know he is, too," said the 37-year-old.
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