The 21-year-old timed 1min 43.74sec to beat Austria’s Mario Matt by 0.87sec with German Alois Vogl 1.48sec back in third.
Byggmark, taking part in only the eighth World Cup slalom of his fledgling career, was in a strong position after posting the fastest time in the first run.
Despite the snowfall and foggy conditions, the young Swede maintained his dominance in the second – and could not contain his joy upon beating all his rivals.
“It’s amazing,” said Byggmark. “I tried not to go into the second run expecting anything and it all worked out. In the second run I was so nervous.
“I could hear people screaming come on, come on, and it is just unbelievable that I won.”
Defending World Cup champion Benjamin Raich of Austria slipped back from second place after the first run to finish fifth, a result that leaves him joint second with Larsson in the slalom standings.
But even Raich would admit the day belonged to Byggmark, who, like Swedish legend Ingemar Stenmark and current women’s alpine queen Anja Pärson, hails from the town of Tärnaby in Sweden’s far north.
Byggmark said he trains occasionally with former World Cup champion Pärson, and he insisted their success was not down to chance.
“It doesn’t date just from today that the Swedes are good in slalom,” he added.
“And it’s not just because of the upcoming world championships are being held in Åre (Sweden) which explains our success.
“We don’t have any secret, it’s down to the programme that’s been put in place for several years. We have a very strong group, that’s all.”
Norway’s Aksel Lund Svindal, 13th here, maintained his position at the top of the overall standings with 745 points in front of Switzerland’s Didier Cuche (677 points) and American Bode Miller (640).