ROC skiers Jūlija Stupaka, Natalija Nepjajeva, Tatjana Sorina and Veronika Stepanova covered the distance in 53 minutes and 41 seconds.
The silver awards were surprisingly won by German skiers Catherine Sauerbrey, Katarina Henniga, Victoria Karl and Sofia Krel, who were still in the lead five kilometers ago, but lost 18.2 seconds to the finish line.
The Swedish Maja Dalquist, Eba Anderson, Frida Carlson and Jonna Sundling, on the other hand, won bronze prizes just before the finish line, beating the fourth-place Finns by only 0.5 seconds.
After a 2.4-kilometer mark, Eiduka was in seventh place, but then clashed with Norwegian skier Tiril Udnes Weng and fell, losing 59.5 seconds to Russian Olympic Committee (ROC) athlete Julia Stupaka after five kilometers.
After two stages, the Germans were in the lead, 4.3 seconds ahead of the ROC skiers, and the third, 22.8 seconds behind, were the Norwegians.
Meanwhile, before the final stage, German skiers had a five-second lead over the ROC, but Norwegian skiers had reduced their deficit to second place by 14.7 seconds.
In the last five kilometers, the victory for ROC skiers was secured by Stepanova, who made a break in the last 1.5 kilometers.
In Latvian skiing, the winners lost seven minutes and 39.6 seconds.
For the first time, Latvia was represented in the women’s ski relay.
In the 2018 Pyongyang Olympics, Norwegian skiers triumphed, followed by the Swedish Quartet and third in the Russian Olympic Committee (ROC).