Pietilä Holmner clocked 1 minute 43.65 seconds to win by just 0.06secs from overall World Cup leader Tina Maze of Slovenia with another Swede, Frida Hansdotter, third 0.32secs off the pace.
For the 28-year-old Swede it was a welcome return to form four years after she won a World Cup slalom in Aspen followed by a parallel slalom in Munich six weeks later.
"It's amazing. This means so much to me and I have proven to myself that I can beat the best again," she said.
"I felt pretty confident. I just promised myself to try and take a chance.
We have such a strong team, both in the slalom and giant, so watch out for Sweden."
US slalom champion Michaela Shiffrin placed fourth after trailing the lead by over half a second on the first run, meaning she remains winless this season.
Maze's second place bolstered her lead in the overall standings. She now has 560 points and is more than 200 points clear at the top.
Maze won the Åre giant slalom on Friday from Sweden's Sara Hector.