Nyman won his second career World Cup event with a time of 1 minute, 28.82 seconds, just 0.19 of a second ahead of Perko, who earned his first career World Cup podium.
"I've always believed I had the speed," Nyman said. "I hope to prove it throughout the year."
Erik Guay of Canada came in third with a time of 1:29.06. Overall points leader Aksel Lund Svindal of Norway took fifth in 1:29.27.
Svindal was among the early starters who had to contend with fog on the slopes. The mist lifted in time to give Nyman, Perko and the other late starters better visibility.