The 34-year-old Matt, a two-time slalom world champion, finished with a combined time of 1min 41.84sec to close the skiing competition.
His compatriot Marcel Hirscher, the reigning world champion, finished second at 0.28sec, with young Norwegian sensation Henrik Kristoffersen taking bronze at 0.83sec.
While Matt beat Norwegian legend Kjetil Andre Aamodt for the mantle of oldest winner, 19-year-old Kristoffersen became the youngest Olympic medallist in men’s alpine skiing.
A legion of favourites failed to finish the second run including Felix Neureuther, Alexis Pinturault and newly-crowned giant slalom champion Ted Ligety.
Away from the slopes, the Olympics were hit by a third doping case after Ukrainian cross country skier Marina Lisogor tested positive for the banned substance trimetazidine.
The Ukrainian Olympic Committee said Lisogor, 30, told a disciplinary hearing that she had unwittingly consumed the substance in a medicine.
“I ask forgiveness from those who will see this and be disappointed or upset. But there was no intent or desire to take a banned substance,” she said.
“It is stupid, accidental. I am sorry there is a scandal but there was no bad intent.”
The case came a day after news of failed tests for German biathlete Evi Sachenbacher-Stehle and Italian bobsledder William Frullani.
Meanwhile, South Korea want the International Skating Union to review whether the decision to award women’s figure skating gold to Russia’s Adelina Sotnikova rather than national heroine Kim Yu-Na was accurate.
Defending Olympic champion Kim was relegated to the silver medal position by the Russian 17-year-old in Thursday’s free skate despite putting in an error-free performance.
It was a decision that prompted accusations of judges being influenced by the passionate support of the crowd.
“The South Korean team in Sochi has politely requested the Korean Skating Union to ask ISU president Ottavio Cinquanta to review the women’s figure skating singles (to see) if it followed the rules of ISU standards,” said a statement from the South Korean body.
Norwegian cross country skier Marit Bjoergen won the women’s 30km mass start, taking her sixth Olympic gold and equalling the record number of medals for a woman at Winter Games.
In a clean sweep for Norway, Bjoergen showed her usual supremacy in the sprint finish, coming home ahead of Therese Johaug and Kristin Stoermer Steira.
Bjoergen has now equalled the record of Soviet speed skater Lidia Skoblikova and Russian cross country skier Lyubov Yegorova in taking six golds at Winter Olympics, the most by any female athlete.
She has also equalled the record of 10 medals overall held by cross country skiers Stefania Belmondo of Italy and Raisa Smetanina of the USSR.
Her compatriot, Ole Einar Bjoerndalen missed out on a chance for a historic ninth gold medal in the men’s 4×7.5km relay.
Four teams were neck-and-neck on the final leg but Norway’s anchorman Emil Hegle Svendsen endured a disastrous final standing shoot that put his team out of the running.
Russian home favourite Anton Shipulin secured the gold by sprinting clear of Germany’s Simon Schempp in the home straight, finishing in 1 hour 12min 15.9sec with Germany 3.5 sec behind. Austria took the bronze.
Bjoerndalen set a record at these Games by winning a total of 13 medals at Winter Olympics but remains equal with Norwegian cross country skier Bjoern Daehlie on the most golds at eight.
Russia’s American-born snowboarder Vic Wild claimed his second gold in Sochi as he stormed to parallel slalom victory while Austria’s Julia Dujmovits took the women’s title.
The Dutch won both men’s and women’s team pursuit titles in a fitting end to a dominant showing in Sochi.
The Netherlands won 23 of the 36 medals on offer, bagging eight of the 12 golds.
In men’s ice hockey, Teemu Selanne scored twice as Finland crushed the USA 5-0 to claim the bronze medal.