Kirchgasser led after the first leg and increased her advantage in the second, finishing in a time of 1 minute, 47.25 seconds, more than sixth-tenths of a second faster than Finland's Tanja Poutiainen. Veronika Zuzulova of Slovakia was third, 1.34 seconds off the pace.
It is Kirchgasser's second career World Cup victory and comes five years after her first triumph in a giant slalom.
"I did pretty good skiing," Kirchgasser said. "I like it when it's icy like this and you have to fight from start to finish. It's a great feeling, it's unbelievable, it's a long time since I won.
"If I'm honest I was a bit scared this morning as it's nine meters high and I haven't really trained much on it but I just thought come on, ski fast and have fun."
World slalom champion Schild had won the previous five World Cup slalom races, while Hoefl-Riesch is the reigning Olympic champion as well as the current World Cup holder. However, both skied out after missing the same gate at the top of the difficult Kranjska Gora course.
A women's World Cup race has only been held on the course twice in the last 21 years, although the men race here regularly.
Schild and Hoefl-Riesch were among 26 competitors who did not finish the first run, while six others failed on the second, including three of the top ten after the first run.
"I don't know if Marlies would have been faster but I had two good runs and gave all I can do," Kirchgasser said. "I don't know if she would have beat me or I would have beat her."
World Cup leader Lindsey Vonn struggled at the bottom of the course, as she did in Saturday's giant slalom, but managed a seventh-place finish with a time of 1:50.14.
"My second run wasn't great — again. And I had problems — again. But I fought really hard," Vonn said. "I gave it my all and pushed all the way but then unfortunately I had problems at the bottom again and I didn't quite do it. I really tried though, and seventh is my best result all season so I'm happy with it."
Home favourite Tina Maze, spurred on by a noisy crowd, finished fourth, slightly cutting Vonn's lead in the overall standings. The American is 282 points ahead of Maze, and is firmly on course for a fourth World Cup title.
"Tina hasn't closed the gap by much, I'm still nearly almost 300 points ahead of her," Vonn said. "And my goal this season is to keep winning in the downhill, keep winning in the super G, win in the super combined ... stay in the top three in the GS and try to stay with her in the slalom.
"She's always top three in the slalom, though not today, so it's going to be tough. But my aim isn't scoring the big points in slalom but just to keep going and stay with her."
The 48th Golden Fox event was supposed to be held in Maribor but was moved due to a lack of snow. Last year's event was also affected by weather and had to be cancelled.
Kathrin Zettel of Austria won the giant slalom and the slalom in 2010. The defending champion finished fifth after a strong second run.
Back in 17th spot after the first run, Zettel was provisional leader with a time of 1:49:53 until overtaken by Maze, the fourth last skier to race.