The 34-year-old clinched the title ahead of his compatriot and hot favourite Marcel Hirscher, who is ten years his junior.
Though a two-time slalom world champion, Matt’s recent showings on the FIS World Cup circuit had done nothing to indicate he would be in contention for the podium in Sochi.
However, in the two runs at Rosa Khutor he proved unbeatable, finishing with a combined time of 1 minute 41.84 seconds to provide the Alpine skiing programme at Sochi 2014 with a suitably dramatic finale.
Hirscher, the reigning world champion, finished second at 0.28 seconds, with young Norwegian sensation Henrik Kristoffersen also coming out of nowhere to take bronze at 0.83 seconds.
“Everything has to fit together and I was lucky in this case. I thought that today I would just ski and just see what happens," said Matt, whose two world titles had come back in 2001 and 2007.
“I approached the course with that attitude and it worked out. It's the highlight of my career.”
Oldest and youngest
Matt overtook Norwegian legend Kjetil Andre Aamodt as the oldest winner of an Alpine event. At the other end of the age spectrum, 19-year-old Kristoffersen became the youngest ever male skier to finish on an Olympic podium.
“I feel pretty good right now,” said the 19-year-old. “It was the goal to be here at the Olympics and, hopefully, I have few more to go. This is unbelievable.”
It completed a remarkable weekend for skiers at both ends of the age spectrum, after US teenager Mikaela Shiffrin had smashed the record for youngest ever Olympic slalom champion the day before.
Kristoffersen, who had won the last slalom going into the Olympics, was 15th after the first run but showed off a commanding performance to take the lead in the second.
But his lead didn't last long as Hirscher, with his typical attacking style, stormed down the course.
The Austrian slalom World Cup winner had made a faultless first run, but had then found himself in ninth place before battling back in impressive fashion.
Felix Neureuther (GER) and Alexis Pinturault (FRA) both failed to complete the two runs, as did newly crowned giant slalom champion Ted Ligety (USA) and defending Olympic champion Giuliano Razzoli (ITA).