The 26-year-old native of Mühlebach in the canton of Valais finished ahead of Japan’s Tomoka Takeuchi and Russia’s Alena Zavarzina at the Rosa Khutor Extreme Park.
Kummer was heavily favoured to win after dominating the Alpine snowboard World Cup for the past three years.
But she sounded almost surprised at the result.
"I cannot believe it," Kummer told Swiss media.
"I am speechless," she said.
"I knew that I could grab it if I stayed calm."
Meanwhile, Swiss Nevin Galmarini earned a silver medal in the men’s parallel giant slalom.
Galmarini, 27, from the canton of Basel-Country, finished behind Russia’s Vic Wild and ahead of Zan Kosir of Slovenia.
Wild is married to Zavarzina making their performances in the men’s and women’s parallel giant slalom a family triumph.
The six gold medals won so far by Switzerland equal the country’s best performance at the Olympics at the 2010 Vancouver Games.
But Wednesday’s results followed disappointments for the Swiss men's ice hockey team, which was knocked out of competition after being stunned by Latvia 3-1 on Tuesday.
The women's hockey team faces Sweden for the bronze medal after losing 3-1 to Canada, who play the US in the gold medal game on Thursday.
In the men’s giant slalom ski race on Wednesday, defending Olympic champion and member of the Swiss team Carlo Janka, was unable to repeat the performance, finishing 13th in a competition won by America’s Ted Ligety.
France's Steve Missiler and Alexis Pinturault came second and third respectively.