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.
The Sochi 2014 downhill winner Mayer 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.
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 a 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.
Jansrud's silver 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.
But there was disappointment for America's four-time Olympian Ted Ligety, who won his first World Cup race in Pyeongchang in 2006, as he failed to finish his run.
Svindal, 35, won the men's downhill as the wind-disrupted Pyeongchang skiing races got under way on Thursday, becoming the oldest alpine ski champion in Games history.
America's Mikaela Shiffrin, winner of the delayed women's giant slalom on Thursday, goes again in the slalom on Friday. Both races were postponed due to strong winds earlier in the Games.
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.