Matt, at 34 years and 250 days old, finished second in the season's opening slalom race in Levi, Finland last month but he went one better this time, and in doing so overtook Christian Jagge who had held the previous record at 33 years and 253 days.
Matt's time of 1:44.59 was enough to edge out Mattias Hargin of Sweden while Patrick Thaler was third for Italy.
It was also Matt's 14th World Cup slalom victory, equalling Benni Raich's Austrian record and placing him fifth on the all-time list.
The win puts him top of the overall standings with 180 points after previous leader Marcel Hirscher failed in his bid for his 11th straight World Cup podium after he failed to qualify for the second run.
It was the reigning world champion's first non-podium finish in slalom since March 2012.