The Croat caught a bump in a sharp left turn, lost balance on one ski and slid off course. He got up shortly afterward and skied down into the finish area.
Cuche, a four-time winner on the Streif course, had a time of one minute 58.10 seconds to lead Austria's Klaus Kroell and France's Johan Clarey, who shared second, by 0.30.
Erik Guay of Mont-Tremblant, Que., was the top Canadian in seventh place while Robbie Dixon of Whistler, B.C., was 16th.
The start of training was delayed for more than 20 minutes after a forerunner crashed and had to be airlifted to hospital with a knee dislocation.
A final training session is scheduled for Thursday, followed by the race Saturday.