It was his fourth World Cup win this season and comes less than a month before he is due to retire. At 37, he is currently the oldest winner on the circuit.
The 2009 world champion in the discipline beat Hudec by 00.16 secs and Raich by 00.21 secs on a rapidly-deteriorating, sun-drenched piste to win his 21st World Cup victory.
In doing so, Cuche climbed to second spot in the overall World Cup super-G rankings, behind the Olympic champion Aksel Lund Svindal of Norway, who was eighth on Friday.
Switzerland's Beat Feuz, one of the three great pretenders for the trophy, had a bad start to his weekened and only took 10 points, which was not enough to knock Austria's Marcel Hirscher from top spot in the general classification.
The race began disastrously with three of the first eight skiiers falling at the start: Switzerland's Patrick Küng and Sandro Viletta, as well as Andreas Romar from Finland.