The 19-year-old, guided by Jennifer Kehoe, took the women's slalom vision impaired title to add to her two silvers and a bronze earlier in the competition, in the process denying Slovakia's Farkasova a fifth gold medal.
Compatriot Millie Knight and her guide Brett Wild also made the podium with their bronze taking the British tally in Pyeongchang to seven medals - their target for the event - on day nine.
Fitzpatrick, whose day did not start as she may have hoped when a ski boot fell on her head, told Paralympics GB's official website: "This morning, I didn't have the greatest start, you wouldn't have thought it was our day.
"I was exhausted after this whole period of racing. The nerves and the emotion were just overwhelming so that didn't make for a great start.
"We just sang songs and danced and it made me feel a lot better and it seemed to work. We may have been dancing in the start gate!
"We just needed something to make us giggle, and that calmed me down."
Farkasova led by 0.66 seconds after the first run, but Fitzpatrick's second attempt saw her eclipse the leader by 1.32 seconds for a total time of one minute 51.80 seconds.