The women from Ukraine covered the 24 kilometers in 1:10.92.5 to defeat the Russian squad by 26.4 seconds. Norway finished third.
Dzhyma was joined by Vita Semerenko, Valj Semerenko and Olena Pidhrushna in winning effort.
Until Friday Ukraine had only one bronze medal to its credit at these Olympics. A record 21 countries have now won at least one gold at the 2014 Games, two more than the old mark set four years ago in Vancouver.
Four skiers travel six kilometers each in the race and all of them take two turns of five shots each during their trip onto the course. For each miss up to three during each phase of shooting, the contestant can load a bullet and take another try. If more than three shots are missed, however, a penalty loop of 150 meters must be skied for each miscue.
Dzhyma did not have a miss in her 10 shots and when she left the shooting range for the second time she had a lead of almost 10 seconds.
That advantage grew to 26 seconds by the end of her leg. Semerenko and Pidhrushna maintained that advantage over the final 12 kilometers.