In a fast and frenetic event debut, women's winner Natalie Geisenberger, men's champion Felix Loch and doubles gold medallists Tobias Wendl and Tobias Arlt combined with three strong runs to end host nation Russia's hopes of topping the podium.
Russia, led by men's runner-up Albert Demchenko, secured silver, 1.030 seconds behind the winners, and Latvia took bronze in front of a sizeable and vociferous crowd with spectators thronging the vantage points along the curves and switchbacks of the Sanki Sliding Centre track.
Underlining their superiority, Geisenberger, Loch and Wendl and Arlt all recorded the fastest individual times.
"It's a very cool event, to have the chance to win a second medal with the team. And to get a second gold medal, that's the greatest feeling ever," said Geisenberger.
"We had the goal to win many medals but to win all the golds, that's unexpected. I think that's the top of a very very good season for us."
Luge powerhouses Germany's last Olympic gold sweep was in 1998 in Nagano when they won the three events staged.
The relay features one woman, one man and one doubles team from each nation sliding back-to-back-to-back runs. At the finish each athlete makes contact with a touch pad, which automatically opens the start gate for the next team member.
Teething troubles with practicality and timekeeping since the concept of luge relay was born in 2003 had delayed its inclusion in the Olympic programme, but it got a resounding thumbs-up from competitors on Thursday.
Canadian Alex Gough, hiding her crushing disappointment after again just missing the podium, adding another fourth place to her fourth in the singles, said it was a "fun event for us to race".
"It's the most entertaining event for us to race."
Austria's doubles silver medallist Andreas Linger was also a fan.
"Almost every other winter sport has a team event at the Winter Games... finally we have one too," he said after finishing seventh out of 12 nations.