Among the athletes are 30 neutral competitors from Russian Federation, which remains suspended by the IPC over a mass doping scandal.
Farkasova and her guide Natalia Subrtova finished in 1:29.72 minutes, beating second-placed Millie Knight of Britain and her guide Brett Wild by 0.86 sec.
It was Farkasova's sixth Paralympic gold, and she hailed her victory as "great, amazing".
North Korea's first Winter Paralympians did not appear alongside South Korea's team, as happened at the Winter Olympics opening ceremony, after a row over the blue-and-white Korean unification flag.
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In the biathlon - which combines skiing and shooting - U.S. took gold and silver in the women's sit ski, with Kendall Gretcsch coming first and Oskana Masters second.
Patmore easily beat Italian Manuel Pozzerle in the two-man final of the upper limb disability class on Monday to win Australia's first medal of the Games.
And unlike at the Olympic opening ceremony last month, when athletes from the two Koreas entered the stadium as a unified delegation, the nations marched separately after failing to agree Thursday on conditions for a dual march.
Three athletes have competed at every Winter Games since 2006: alpine skiers Laurie Stephens and Tyler Walker, and sled hockey goalie Steve Cash. One day after winning gold in the men's 7.5km sitting biathlon, the former Navy Seal took the silver in the 15k sitting biathlon on Sunday.
North Korea pulled out of the joint march after South Korea made a decision to remove islands claimed by Japan from the flag, which depicts the Korean peninsula.