The 19-year-old rising star notched his first World Cup victory and fourth podium of the season in just his 23rd career race on the circuit.
In the process, he bested established stars Marcel Hirscher of Austria and Germany's Felix Neureuther, who placed second and third, respectively.
"Last year my best finish was an 11th place, it was my first season in World Cup," said Kristofferson, who moved into eighth place in both the men's slalom and overall standings.
Kristofferson finished the night race in 1 minute, 47.43 seconds. Hirscher was clocked at 1:47.61, 1/100th of a second ahead of Neureuther.
The top American finisher was David Chodounsky, who placed 22nd with a 1:51.04.
Celebrity Families of 2014 [PHOTOS]