Braathen, who had never finished in a World Cup podium position, improved from fifth place after the opening leg to upset the pre-race favorites and clinch his first career win.
Braathen posted the second fastest time in the decisive leg to finish ahead of Swiss duo Marco Odermatt and Caviezel.
Competing in only his 23th event in the World Cup, Braathen had a fourth place as his previous best result at the slalom in Kitzbuehel in January.
With Braathen and Odermatt, who turned 23 this month, a younger generation occupied the top spots in the season's first race.
The next World Cup races are parallel events for men and women in another Austrian resort, Lech/Zuers, on Nov. 13-14.