The 34-year-old held his nerve to win by 0.28 seconds over two legs down a Rosa Khutor course that proved too difficult for many of the medal contenders.
World champion Hirscher put down a superb second run to climb from ninth to first with only Matt of the top 30 left to ski, but could only watch as the veteran squeezed home.
Norway's Henrik Kristoffersen, 19, took the bronze medal to become the youngest man to win an Olympic medal in Alpine skiing.
- Sports & Recreation
- Rosa Khutor