Braathen moved up from third after the opening run to finish a slim 0.02 seconds ahead of Norwegian teammate Henrik Kristoffersen on the Gran Risa course.
Calgary’s Erik Read was 21st.
Odermatt, the Olympic champion, defending overall World Cup champion and current leader of the overall standings, recovered from a disappointing ninth in the opening leg to place third, 0.10 behind.
When it was over, Braathen looked like a prize fighter as he unleashed a series of fist pumps to celebrate. Then during the podium celebration when he took his gloves off, Braathen revealed that his fingernails were painted black with the exception of one finger that had a yellow design.
Only two other active male skiers have won a slalom and giant slalom World Cup race in the same season: Kristoffersen and former overall champion Alexis Pinturault.
“It’s incredible. Growing up watching Alta Badia as a kid, it’s one of the favorites. It’s arguably the coolest giant slalom slope in the world,” Braathen said. “I can’t believe I’m victorious here; it’s unbelievable. I’m going to remember this day forever.”
It was Braathen’s fourth career win. His first came in the season-opening giant slalom in Sölden, Austria, two seasons ago. But a serious knee injury later that season set him back and forced him to miss the 2021 world championships in Cortina d’Ampezzo.
Now, Braathen is back on track and shaping up as a medal threat in two races at this season’s worlds in Courchevel and Méribel, France, in February.
Odermatt, who won the opening two giant slaloms this season, extended his lead in the overall standings ahead of Aleksander Aamodt Kilde, who didn’t finish his opening run, to 171 points.
Braathen moved up to third overall, albeit a distant 381 points behind Odermatt.
Pinturault finished fourth and first-run leader Zan Kranjec came fifth.
The surprise of the day belonged to Andorran skier Joan Verdu, who posted a career-best 12th-place finish with the fastest second run.
River Radamus and Tommy Ford, the top American GS skiers, both had trouble in the first run.
Radamus, who finished fourth at the Beijing Olympics, fell down on his left hip on the upper section and didn’t finish. Ford also lost control and had to check his skis to make the next gate, eventually crossing nearly 5 seconds behind.
Another GS is scheduled for the Gran Risa on Monday.
___
More AP skiing: https://apnews.com/hub/skiing and https://twitter.com/AP_Sports
The Associated Press
