Racing against the US, the 33-year-old stumbled on the final lap before slipping headfirst along the Richmond Oval ice and then crawling across the final 25 metres to get over the line, just 0.23sec ahead of the Americans.
In the final, the Japanese team led the Germans for five laps as Stephanie Beckert, Daniela Anschütz Thomas and Katrin Mattscherodt trailed by more than a second.
But in the final 600 metres Germany turned up the heat and crossed the line in 3min 2.82sec to take gold by just 0.02sec.
The Japanese team of Masako Hozumi, Nao Kodaira and Maki Tabata took silver with Poland claiming bronze.
"My feelings are up and down. It was like a carousel. I nearly messed it up," said Friesinger-Postma.
"I thought, 'No, No, I'm falling'. I thought I messed up for the team. I yelled but no one heard me, so I just kept on going."
In the men's event, Canada's Denny Morrison, Lucas Makowsky and Mathieu Giroux took the pursuit gold, their country's first speed skating medal of the Games.