Germany won in 49 minutes, 30.6 seconds.
Norway took the silver - just 1.3 second behind - with Switzerland claiming bronze a further 31.7secs back.
It was the first medal in this event for Germany since the former East Germany won it in 1980.
The Norwegians led after the second and third legs, but Sachenbacher quickly passed Moen on an uphill at the 1.7km mark.
Norway second again
Moen retook the lead just before the skiers entered the stadium and looked like she might pull away.
But Sachenbacher, who won the silver medal in the 1.5km sprint on Tuesday, cruised past the leader with 100 metres to go.
Moen realised she was beaten and coasted across the finish line in second.
The German team consisted of Manuela Henkel, Viola Bauer, Claudia Kuenzel and Sachenbacher.
"I can't believe that we have won the gold medal," Sachenbacher said. "I followed Anite (Moen) for the last two kilometres but I was strong at the finish."
For Norway it was the fourth consecutive time they had been beaten into the runners-up spot.
Meanwhile, favourites and defending champions Russia pulled out of the race after five-time gold medallist Larisa Lazutina was withdrawn following a blood test.
The Russian team immediately launched a protest because they said they had been unable to replace Lazutina in time for the race.
Vitali Smirnov, a Russian vice-president of the International Olympic Committee, said the out of competition test showed Lazutina's red blood cell count was above the level permitted by the International Skiing Federation (FIS).
The Ukraine also failed to start the race but there was no immediate explanation for their withdrawal.