After having achieved 13 podium finishes in 10 years, the former junior world champion finally broke through when she clocked a combined time of one minute 37.28 seconds.
"It's just a lifetime dream come true. I had been on the podium so many times I didn't know if this would finally happen," Velez Zuzulova told reporters.
"I come from a very small country and up to now I was the only one the fans could count on. The pressure was enormous, everybody kept asking me when I would make it at last."
Zuzulova, 28, who married her French coach Romain Velez earlier this year, was 0.10 seconds ahead of Austrian Kathrin Zettel.
Zettel, winner of a slalom in Colorado last month, was cheered wildly by the huge crowd gathered in the closest ski resort to the Austrian capital of Vienna.
Zuzulova said she longed for the day when she would receive a similar kind of support.
"In another life I would love to come back as an Austrian skier to feel what the girls feel here," she said. "It must be great."
Overall World Cup leader Tina Maze was fastest on the first run but skied a little too conservatively in the floodlit second leg and had to be content with third place, 0.20 off the pace.
It was the Slovenian's 11th podium finish of the season and lifted her overall points tally to 1,059, giving her a lead of 427 points over second-placed German Maria Hoefl-Riesch who ended up fourth in Semmering.
There was more good news for Slovakia when Velez Zuzulova's 17-year-old compatriot Petra Vlhova secured 11th position in her first World Cup race.
American teenager Mikaela Shiffrin, who claimed her first World Cup victory in Sweden last week, missed a gate on the second leg and failed to score any points.
The next race is in Munich on New Year's Day, a parallel slalom competition involving the 12 best skiers in the discipline and the top four all-rounders.