Matt, a two-time world slalom champion, turned in a two-run time of 1 minute, 50.35 seconds to edge Herbst and third-place Jean-Baptiste Grange of France.
Grange actually came out well. He moved into position to challenge Ivica Kostelic of Croatia, who leads the overall World Cup points race and the slalom standings but did not finish Sunday's event. Kostelic has 478 points in the slalom and Grange 442 with two more slaloms on the schedule.
"It was sunny and the snow was a lot better than I thought it would be," said Nolan Kasper, the top U.S. finisher who took 10th place. "It was a pretty easy hill so you really had to be gunning from the get-go."
Ted Ligety of the United States was 17th and Christof Innerhofer of Italy did not start the first run.