Mayer seized the lead from Norwegian defending champion Kjetil Jansrud with a blistering descent of 1min 24.44sec. Switzerland's Beat Feuz took silver, 0.13sec adrift, while Jansrud had to settle for bronze.
Norwegian skiers had won five of the eight previous Olympic super-G races, including the last four, and appeared to have locked up another victory when Jansrud bombed down in 1.24:62.
But Mayer, 27, mastered the course to outpace Jansrud by 0.18sec before downhill world champion Feuz, the next man to descend, grabbed second place.
“It was an awesome run, now I have my second gold medal,” said Mayer. “It is most special.”
Mayer, the Sochi 2014 downhill winner, trumps his father, Helmut, who won super-G silver in 1988, and emerges victorious just three days after he ploughed into bystanders during the combined event.
It was a particularly sweet victory for Mayer, who failed to finish the super-G at Sochi 2014 and also at last year's world championships. In between those two events, he fractured a vertebra in 2015.
France's Blaise Giezendanner grabbed a surprise fourth position after briefly occupying second place, while Norway's Axel Lund Svindal, who won the downhill on Thursday, was fifth.
Strong winds have played havoc with the schedule in Pyeongchang and organisers are playing catch-up with the alpine events, meaning a demanding few days for the racers.
“It's always very tough, especially when the races are in such short gap apart,” said the triumphant Mayer.
“We don't know the hills, that always makes us worry, especially in super-G because we only have little training and that makes this medal for me so special.”
Jansrud's medal puts him in joint third place in the all-time list of Olympic skiing medallists, behind only countryman Kjetil Andre Aamodt and America's Bode Miller.
Svindal, 35, won the men's downhill as the wind-disrupted skiing races got under way on Thursday, becoming the oldest alpine ski champion in Games history.
Norway have ruled the physically demanding super-G in Olympic competition since the turn of the century, winning in 2002, 2006, 2010 and 2014, as well as 1992.
Friday's race was held over the Jeongseon Downhill course, which plunges 650m in altitude over two kilometres (1.24 miles) in a scenic valley in the Pyeongchang mountains.