On a day when the big favourites failed to shine, Italy's Christof Innerhofer took the silver and Norwegian Kjetil Jansrud the bronze.
Mayer, who started 11th, is the son of 1988 super-G silver medallist Helmut. His gold medal provided an immediate boost for a men's team who failed to win a single medal in Vancouver four years ago.
Favourites Bode Miller of the United States and Norway's Aksel Lund Svindal, the downhill world champion and 2010 silver medallist, failed to live up to their pre-race billing on an overcast day on the Rosa Khutor piste.
Miller, 36, was bidding to become the oldest man to win an Alpine gold at a Games but was eighth after all the top skiers had finished.
(Reporting by Alan Baldwin, editing by Peter Rutherford)
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