The Russians took biathlon relay gold in Vancouver 2010 but had yet to finish on the podium in the two previous World Cup 4x6km relay races this season.
But the quartet of Ekaterina Glazyrina, Olga Zaitseva, Irina Starykh and Olga Vilukhina took victory in impressive style on Wednesday, posting an overall time of 1:09.42.2hours.
It was enough to see them take victory over home favourites Germany by 6.2 seconds while Norway completed the medal podium 16.7 seconds behind the leaders for bronze.
Germany, who won the previous relay event in Annecy-Le Grand Bornand last month, continue to top the overall standings with 168 points ahead of Ukraine, who finished fourth in Germany.
Meanwhile Russia's victory sees them move up to third in the standings with 141 points.