That success ended American hopes of a 1-2, pushing their two teams into the silver and bronze positions.
Lange, competing in his first Olympics, ended the competition with a combined four-run time of three minutes 7.51 seconds.
It completed Germany's dominance of the bobsleigh events with Christoph Langen having piloted Germany 1 to success in the two-man competition earlier in the Games.
Todd Hays, the pilot of US1, had seen his team take command midway through the event, before losing the lead on the third run.
Afterwards Lange admitted that proved a decisive moment.
"It's so incredible," he said. "We did not really believe that we could win because we were quite a bit behind.
"But we had an extraordinary third run. I don't know what to say. We have to let it settle for a while."
"I can't put this into words. Two medals - there is no better time to be an Olympian than right now."
Todd Hays on America's 1-2
Lange's success ended a topsy-turvy 24 hours for Germany in the event.
His team-mate Langen, looking to add to his two-man gold and defend his Olympic four-man title too, was forced to withdraw his Germany 1 crew from the final two heats after he injured a foot on Friday.
He had been lying seventh.
Hays, who had been looking to give the US their first gold medal in the four-man event since St Moritz in 1948, was still content with their first gong since a bronze in 1956.
Bursting into tears after the final run he said: "I can't put this into words. Two medals - there is no better time to be an Olympian than right now."
Hays finished 0.30 secs behind Lange with Shimer a further 0.05 secs back.