Just two weeks after coming second in a giant slalom in Are, Sweden, Hector upset all pre-race favourites to win a GS on Sunday.
"I am a bit surprised," said the 22-year-old Hector, who won the junior world title in the discipline in 2011. "It's not easy to put words on it. It's emotionally different from Are as my family was there. It's just crazy that it's all happening."
On a course new to the World Cup, Hector finished in a combined time of 2 minutes, 17.61 seconds to beat Anna Fenninger of Austria by 0.09 seconds.
American teenager Mikaela Shiffrin, who led after the opening run, came 0.18 behind in third while Marie-Pier Prefontaine of St-Sauveur, Que., was a career-best sixth place. Tina Maze of Slovenia was seventh to remain in the lead of the overall standings.
"I am skiing well all season and luckily it's now showing in the races, too," Hector said. "I have developed, I am mentally and physically stronger, and my equipment and set-up are good."
Hector, who posted the fifth-fastest time in the second leg, trailed Shiffrin by 0.27 after the opening run, but the American lost a piece of her advantage at every split time of her final run.
Shiffrin still led by 0.04 at the last intermediate time but didn't pick the fastest line toward the finish and dropped to third, acknowledging she lost "maybe one-tenth" there.
Hector's win was "not a big surprise" to Fenninger, the defending overall champion from Austria said.
"I expected her back on the podium soon," said Fenninger, who struggled with the aftermath of a cold. "I've been a bit ill during the holidays. I have to be careful with my energy."
The win saw Hector rise to fourth in the GS standings with 219 points, just seven behind Shiffrin. Eva-Maria Brem of Austria, who finished fourth, kept the lead with 270 points ahead of Fenninger with 242.
Shiffrin was chasing her second win in GS and 11th overall after leading the opening run.
The American is Olympic and world champion in slalom and has earned the discipline World Cup title for two straight years but is yet to reach a podium in her strongest event this season. In GS, however, she has vastly improved.
"I love skiing GS right now, especially when I ski well, but it's not my favourite," Shiffrin said. "I am satisfied to be on the podium again. I attacked (the second run) just enough to get a podium."
Maze, who won the previous GS two weeks ago, improved to seventh after finishing a disappointing first run in 13th, while world champion Tessa Worley of France came 28th.
Marie-Michele Gagnon of Lac-Etchemin, Que., was 19th.
It was the fourth women's GS of the season but the last before the world championship race in Beaver Creek on Feb. 12.
The event was initially scheduled for Semmering but had to be moved because of a lack of snow in the resort near Vienna. It's the first World Cup event in Kuehtai, which hosted lower-tier Europa Cup races before and was a venue for the inaugural Winter Youth Olympics in nearby Innsbruck in 2012.
A slalom on the same course is scheduled for Monday.