The Austrian topped the leaderboard after the first run and was boosted by several top contenders crashing out, meaning he had a cushion of 1.28 seconds before setting off second time around.
His final run was exactly one second slower than silver medallist and fellow Austrian Marcel Hirscher, but it was enough to ensure, at 34 years and 319 days old, he overtook the record previously held by Norway's Kjetil Andre Aamodt, who was 34 years and 169 days when he triumphed in the men's super G at the Turin Games in 2006.
Conversely, Henrik Kristoffersen became the youngest medallist at an alpine skiing event as his bronze, at 19 years and 235 days old, ensured he beat the record of Alfred Matt, who was 19 years old and 282 days when he finished third in the men's slalom in the 1968 Games.
Despite being a two-time world slalom champion - in 2001 and 2007 - Mario Matt had never finished higher than 34th at a Games before Saturday.
"You can tell yourself this is just a training run but when it works out like this it is incredible. A massive goal has come through for me," he said.
"Everything has to fit together and I was lucky in this case," he added.
"I thought that today I would just ski and just see what happens. I approached the course with that attitude and it worked out."
An overall time of one minute, 41.84 seconds was enough to finish 0.28secs clear of pre-event favourite Hirscher, who was going into the event as the reigning world champion and World Cup leader.
Hirscher was ninth after the first run, although was boosted when five of the eight people above him - including the much fancied trio of Alexis Pinturault, Felix Neuruether and Ted Ligety - crashed out second time around.
"With the time I was behind I thought this would be impossible but I managed to get my skiing back to normal and luckily the snow got a bit harder and I managed to make up a lot of time," said Hirscher.
"I am immensely relieved."
With only 43 finishers out of 117 starters, the course at the Rosa Khutor Alpine Center has attracted some criticism, although Hirscher was grateful.
"During the inspection, I could see that there was a big potential for mistakes and for some people it worked out and others it didn't," he added.
"Thank God it was that selective, otherwise this would have never been possible."
Teenager Kristoffersen was 15th after his first run but was delighted after a superb second run bumped him up to a podium spot.
He said: "I feel pretty good right now. It was the goal to be here at the Olympics and, hopefully, I have a few more to go. This is unbelievable."