Overall World Cup leader Marcel Hirscher finished 2.19 seconds back in third but still extended his lead over Alexis Pinturault to 268 points at the top of the standings, after the Frenchman finished the slalom in ninth.
"It is possible to beat me but today I was skiing well," Kristoffersen said after his win, which now sees him go level with Hirscher at the top of the slalom standings.
Thick fog hindered the skiers throughout the day, although the Norwegian had a clearer morning run than Austrian rival Hirscher who was visibly frustrated when crossing the line.
"Of course it's not 100% fair," Kristoffersen said of the fog. "But that goes back and forth if you are skiing for many years."
The victory in tricky conditions was redemption of sorts for Kristoffersen, after his hopes of winning in Zagreb, Croatia last week were ended by high winds.
It was the 22-year-old's 13th career World Cup win, 12 of which have come in the slalom.
Shiffrin stars in Maribor
Meanwhile, US star Mikaela Shiffrin edged out Wendy Holdener in the ladies' slalom at Maribor, Slovenia.
Shiffrin finished just 0.19 seconds ahead of her Swiss opponent to extend her lead over Lara Gut to 305 points at the top of the overall standings.
Gut, who won the World Cup title last season, was third in Saturday's giant slalom but failed to qualify for the second run on Sunday.
"It was really nice to ski. It was a quick course and the surface is awesome, so definitely fun. High fun factor, and I think I can move quicker," Shiffrin, who was fourth on Saturday, told FIS Ski.
"I'm motivated by others, for sure, but I was motivated just as much last year as I am right now.
"When I was a kid, I dreamed about being the best in the world in all the different events."
Shiffrin also had to overcome a broken gate on the course, which went between her legs and under her skis, causing her to fall behind Holdener.
However, the 21-year-old rallied in the final section to eventually pull 0.19 seconds clear.
Sweden's Frida Hansdotter completed the podium with her first top-three finish of the season.
The women now travel to Flachau, Austria where they will again compete in the slalom.