Matt, who had won every one of his heats on the way to the finals, moved up from third to second when he passed home favourite Jean Frederic Chapuis with only two turns remaining.
He then proceeded to catch Victor Oehling Norberg over the last jump to claim the win in a photo finish on the line, while Chapuis took third.
It moves Matt, whose older brother Mario won the Val D'Isere World Cup slalom event on the same weekend, up to second in the overall standings on 105 points, five behind Chapuis.
Jonas Devouassoux, winner of the opening event in Nakiska earlier this month and third overall, finished down in 61st.
"I'm really happy to win this race today, and happy to be back on the podium," said Matt. "Last year was tough for me, I had some things going on, little things, but I didn't ski well.
"This summer I trained differently and lost some kilos and I feel good on my skis again. This win feels good."
In the women's race, Katrin Mueller worked her way through the field to take the second victory of her career.
The Swiss skier pushed compatriot Sanna Luedi into second, while Ophelie David took the bronze to provide some cheer for the home crowd.
Marielle Thompson continues to lead the overall standings with 145 points ahead of David after following up her opening win in her native Canada with fifth place in France.