The Czech turned in a combined two-run time of 1 minute, 37.28 seconds, in good conditions at Semmering, topping Kathrin Zettel of Austria by 1/10th of a second.
Zuzulova finished the first round in 47.77 but was clocked at 49.51 in the second trip.
Tina Maze of Slovenia took third with a 1:37.48. The overall World Cup points leader had led after her first run of 47.22 despite whacking her arm on a gate, but turned in a disappointing 50.26 in the second try.
Germany's Maria Hoefl-Riesch finished fourth at 1:38.39.
It was a tough day for the U.S. women's team. Hailey Duke and rising star Mikaela Schiffrin failed to finish and Resi Stiegler finished 26th.
Notable deaths of 2014 [PHOTOS]