With impressive shooting over the final half of the race, the German team, anchored by Kati Wilhelm, triumphed in the event they won in Nagano in 1998.
The pre-race favourites, which also included Katrin Apel, Uschi Disl and Andrea Henkel, covered the distance in one hour, 27 minutes, 55 seconds, 30.6 seconds ahead of Norway in second.
Russia narrowly beat Bulgaria for bronze, finishing 1:24.7 minutes further back.
"Usually when we start as bad as that it turns out
pretty good in the end"
The victory also marked Wilhelm's third medal of the Games, having already won the women's 7.5 km sprint and grabbed a silver in the 10 km pursuit.
After bringing back two of the four biathletes from the winning 1998 team, the Germans were the heavy favourites to capture the event again.
But Apel's disastrous first leg saw them drop as low as 12th at one stage.
The Nagano veteran missed one target after using her three extra bullets - which in the relay have to be loaded by hand individually - and consequently had to ski a penalty loop.
"I'm very angry about that and I hope my other three teammates will bring Germany back to the podium," she said shortly after handing over to fellow Nagano team-mate Disl.
If the rest of the German team were upset with Apel, they certainly did not show it.
"It didn't bother me that Katrin had the missing shots," Disl said. "Usually when we start as bad as that it turns out pretty good in the end."
Disl, chasing her eighth Olympic medal, soon had them back in front after her first shoot and individual 15 km gold medallist Henkel kept the lead.
Henkel, who won the gold medal in the 15Km last week, hit all 10 of her targets and when she tapped teammate Wilhelm to begin the final 7.5K leg, Germany had a commanding 38.6-second lead over Norway.
Wilhelm gave the Norwegians a chance to make up the time when she missed two shots on the firing rance, but Liv Grete Poiree failed to capitalize after she missed twice as well.
She left the range 42.8 seconds back, with no hope of catching Wilhelm, who raced over the finish line to claim Germany's second successive Olympic 4x7.5km title.