Trailing 10-6 overnight, Jose Maria Olazabal's side needed to match the largest last-day comeback in the event's history - achieved by the home side at Brookline in 1999 - to take the trophy back from Chicago.
And they did so in incredible style, winning the first five singles matches and adding further wins from Sergio Garcia and Lee Westwood before Kaymer secured the decisive point on the 18th by beating Steve Stricker.
The final match between Tiger Woods and Francesco Molinari was halved when Woods missed a close-range par putt on the last, giving Europe outright victory by 14.5 points to 13.5
"It's a feeling I've never had before," Kaymer said. "On Friday I sat down with Bernhard and talked to him about the Ryder Cup because my attitude was not the right one, but after that I know how important the Ryder Cup is."
Langer had missed a putt of six feet to secure the cup at Kiawah Island in 1991, but his fellow German somehow held his nerve from the same distance after charging his birdie attempt past the hole.
Asked to compare the win to his US PGA triumph in 2010, Kaymer added: "It's a completely different level. The major was just for me. Here, my brother and father were here and now I know how great it feels to win the Ryder Cup."
Justin Rose, who birdied the last two holes to beat Phil Mickelson, said: "We are in shock.
"We wanted to believe, we really did want to believe, but we had no illusions of how hard that day was going to be; four points against a team that's played so well all week."
Ian Poulter, who also won the last two holes to defeat Webb Simpson and make it four wins out of four this week, added: "Ollie said to us at the start of the week, Ryder Cup is what memories and dreams are made of, and he's been awesome.
"And last night [Saturday] in that team room was buzzing. We weren't four down. We were all square. We just knew we had a chance and do you know what? This is history right here. This has been unbelievable.
"I'm going to enjoy it, with the best team I've ever seen, and the best captain I've ever seen, and everyone else, because this right here is special."